1. Use Cramer's Rule to solve the following system. x+y+z=0 2x - y + z = -1 -x + 3y - z = -8 A. {(-1, -3, 7)} B. {(-6, -2, 4)} C. {(-5, -2, 7)} D. {(-4, -1, 7)} 2. Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 5x + 8y - 6z = 14 3x + 4y - 2z = 8 x + 2y - 2z = 3 A. {(-4t + 2, 2t + 1/2, t)} B. {(-3t + 1, 5t + 1/3, t)} C. {(2t + -2, t + 1/2, t)} D. {(-2t + 2, 2t + 1/2, t)} 3. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. x - 2y + z = 0 y - 3z = -1 2y + 5z = -2 A. {(-1, -2, 0)} B. {(-2, -1, 0)} C. {(-5, -3, 0)} D. {(-3, 0, 0)} 4. Use Gauss-Jordan elimination to solve the system. -x - y - z = 1 4x + 5y = 0 y - 3z = 0 A. {(14, -10, -3)} B. {(10, -2, -6)} C. {(15, -12, -4)} D. {(11, -13, -4)} 5. Use Cramer's Rule to solve the following system. 2x = 3y + 2 5x = 51 - 4y A. {(8, 2)} B. {(3, -4)} C. {(2, 5)} D. {(7, 4)} 6. Use Cramer's Rule to solve the following system. 12x + 3y = 15 2x - 3y = 13 A. {(2, -3)} B. {(1, 3)} C. {(3, -5)} D. {(1, -7)} 7. Use Cramer's Rule to solve the following system. x + 2y = 3 3x - 4y = 4 A. {(3, 1/5)} B. {(5, 1/3)} C. {(1, 1/2)} D. {(2, 1/2)} 8. Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. w - 2x - y - 3z = -9 w+x-y=0 3w + 4x + z = 6 2x - 2y + z = 3 A. {(-1, 2, 1, 1)} B. {(-2, 2, 0, 1)} C. {(0, 1, 1, 3)} D. {(-1, 2, 1, 1)} 9. Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 3x + 4y + 2z = 3 4x - 2y - 8z = -4 x+y-z=3 A. {(-2, 1, 2)} B. {(-3, 4, -2)} C. {(5, -4, -2)} D. {(-2, 0, -1)} 10. Use Cramer's Rule to solve the following system. 4x - 5y = 17 2x + 3y = 3 A. {(3, -1)} B. {(2, -1)} C. {(3, -7)} D. {(2, 0)} 11. Use Cramer's Rule to solve the following system. 3x - 4y = 4 2x + 2y = 12 A. {(3, 1)} B. {(4, 2)} C. {(5, 1)} D. {(2, 1)} 12. Use Cramer's Rule to solve the following system. x+y= 7 x-y=3 A. {(7, 2)} B. {(8, -2)} C. {(5, 2)} D. {(9, 3)} 13. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. x + y - z = -2 2x - y + z = 5 -x + 2y + 2z = 1 A. {(0, -1, -2)} B. {(2, 0, 2)} C. {(1, -1, 2)} D. {(4, -1, 3)} 14. Use Gaussian elimination to find the complete solution to each system. 2x + 3y - 5z = 15 x + 2y - z = 4 A. {(6t + 28, -7t - 6, t)} B. {(7t + 18, -3t - 7, t)} C. {(7t + 19, -1t - 9, t)} D. {(4t + 29, -3t - 2, t)} 15. Use Gaussian elimination to find the complete solution to each system. x1 + 4x2 + 3x3 - 6x4 = 5 x1 + 3x2 + x3 - 4x4 = 3 2x1 + 8x2 + 7x3 - 5x4 = 11 2x1 + 5x2 - 6x4 = 4 A. {(-47t + 4, 12t, 7t + 1, t)} B. {(-37t + 2, 16t, -7t + 1, t)} C. {(-35t + 3, 16t, -6t + 1, t)} D. {(-27t + 2, 17t, -7t + 1, t)} 16. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. 3x1 + 5x2 - 8x3 + 5x4 = -8 x1 + 2x2 - 3x3 + x4 = -7 2x1 + 3x2 - 7x3 + 3x4 = -11 4x1 + 8x2 - 10x3+ 7x4 = -10 A. {(1, -5, 3, 4)} B. {(2, -1, 3, 5)} C. {(1, 2, 3, 3)} D. {(2, -2, 3, 4)} 17. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. 2x - y - z = 4 x + y - 5z = -4 x - 2y = 4 A. {(2, -1, 1)} B. {(-2, -3, 0)} C. {(3, -1, 2)} D. {(3, -1, 0)} 18. Use Cramer's Rule to solve the following system. 4x - 5y - 6z = -1 x - 2y - 5z = -12 2x - y = 7 A. {(2, -3, 4)} B. {(5, -7, 4)} C. {(3, -3, 3)} D. {(1, -3, 5)} 19. Give the order of the following matrix; if A = [aij], identify a32 and a23. 1 -5 e 0 7 -6 - -2 1/2 11 -1/5 A. 3 * 4; a32 = 1/45; a23 = 6 B. 3 * 4; a32 = 1/2; a23 = -6 C. 3 * 2; a32 = 1/3; a23 = -5 D. 2 * 3; a32 = 1/4; a23 = 4 20. Find the products AB and BA to determine whether B is the multiplicative inverse of A. 0 1 0 A= 0 0 1 1 0 0 0 0 1 B= 1 0 0 0 1 0 A. AB = I; BA = I3; B = A B. AB = I3; BA = I3; B = A-1 C. AB = I; AB = I3; B = A-1 D. AB = I3; BA = I3; A = B-1 21. Find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: (0, -3), (0, 3) Vertices: (0, -1), (0, 1) A. y2 - x2/4 = 0 B. y2 - x2/8 = 1 C. y2 - x2/3 = 1 D. y2 - x2/2 = 0 22. Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis vertical with length = 10 Length of minor axis = 4 Center: (-2, 3) A. (x + 2)2/4 + (y - 3)2/25 = 1 B. (x + 4)2/4 + (y - 2)2/25 = 1 C. (x + 3)2/4 + (y - 2)2/25 = 1 D. (x + 5)2/4 + (y - 2)2/25 = 1 23. Convert each equation to standard form by completing the square on x and y. 4x2 + y2 + 16x - 6y - 39 = 0 A. (x + 2)2/4 + (y - 3)2/39 = 1 B. (x + 2)2/39 + (y - 4)2/64 = 1 C. (x + 2)2/16 + (y - 3)2/64 = 1 D. (x + 2)2/6 + (y - 3)2/4 = 1 24. Find the standard form of the equation of each hyperbola satisfying the given conditions. Endpoints of transverse axis: (0, -6), (0, 6) Asymptote: y = 2x A. y2/6 - x2/9 = 1 B. y2/36 - x2/9 = 1 C. y2/37 - x2/27 = 1 D. y2/9 - x2/6 = 1 25. Find the focus and directrix of each parabola with the given equation. x2 = -4y A. Focus: (0, -1), directrix: y = 1 B. Focus: (0, -2), directrix: y = 1 C. Focus: (0, -4), directrix: y = 1 D. Focus: (0, -1), directrix: y = 2 26. Find the vertex, focus, and directrix of each parabola with the given equation. (y + 1)2 = -8x A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2 B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3 C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1 D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5 27. Convert each equation to standard form by completing the square on x or y. Then nd the vertex, focus, and directrix of the parabola. y2 - 2y + 12x - 35 = 0 A. (y - 2)2 = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9 B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6 C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6 D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8 28. Convert each equation to standard form by completing the square on x or y. Then nd the vertex, focus, and directrix of the parabola. x2 - 2x - 4y + 9 = 0 A. (x - 4)2 = 4(y - 2); vertex: (1, 4); focus: (1, 3) ; directrix: y = 1 B. (x - 2)2 = 4(y - 3); vertex: (1, 2); focus: (1, 3) ; directrix: y = 3 C. (x - 1)2 = 4(y - 2); vertex: (1, 2); focus: (1, 3) ; directrix: y = 1 D. (x - 1)2 = 2(y - 2); vertex: (1, 3); focus: (1, 2) ; directrix: y = 5 29. Find the standard form of the equation of the following ellipse satisfying the given conditions. Foci: (-2, 0), (2, 0) Y-intercepts: -3 and 3 A. x2/23 + y2/6 = 1 B. x2/24 + y2/2 = 1 C. x2/13 + y2/9 = 1 D. x2/28 + y2/19 = 1 30. Locate the foci and find the equations of the asymptotes. x2/9 - y2/25 = 1 A. Foci: ({36, 0) ;asymptotes: y = 5/3x B. Foci: ({38, 0) ;asymptotes: y = 5/3x C. Foci: ({34, 0) ;asymptotes: y = 5/3x D. Foci: ({54, 0) ;asymptotes: y = 6/3x 31. Find the vertex, focus, and directrix of each parabola with the given equation. (x - 2)2 = 8(y - 1) A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1 B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1 C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1 D. Vertex: (2, 3); focus: (4, 3); directrix: y = -1 32. Find the standard form of the equation of the following ellipse satisfying the given conditions. Foci: (0, -4), (0, 4) Vertices: (0, -7), (0, 7) A. x2/43 + y2/28 = 1 B. x2/33 + y2/49 = 1 C. x2/53 + y2/21 = 1 D. x2/13 + y2/39 = 1 33. Find the solution set for each system by finding points of intersection. x2 + y2 = 1 x2 + 9y = 9 A. {(0, -2), (0, 4)} B. {(0, -2), (0, 1)} C. {(0, -3), (0, 1)} D. {(0, -1), (0, 1)} 34. Locate the foci of the ellipse of the following equation. 25x2 + 4y2 = 100 A. Foci at (1, -11) and (1, 11) B. Foci at (0, -25) and (0, 25) C. Foci at (0, -22) and (0, 22) D. Foci at (0, -21) and (0, 21) 35. Find the focus and directrix of the parabola with the given equation. 8x2 + 4y = 0 A. Focus: (0, -1/4); directrix: y = 1/4 B. Focus: (0, -1/6); directrix: y = 1/6 C. Focus: (0, -1/8); directrix: y = 1/8 D. Focus: (0, -1/2); directrix: y = 1/2 36. Locate the foci and find the equations of the asymptotes. x2/100 - y2/64 = 1 A. Foci: ({= 221, 0); asymptotes: y = 2/5x B. Foci: ({= 231, 0); asymptotes: y = 4/7x C. Foci: ({= 241, 0); asymptotes: y = 4/7x D. Foci: ({= 241, 0); asymptotes: y = 4/5x 1. Use Cramer's Rule to solve the following system. x+y+z=0 2x - y + z = -1 -x + 3y - z = -8 A. {(-1, -3, 7)} B. {(-6, -2, 4)} C. {(-5, -2, 7)} D. {(-4, -1, 7)} 2. Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 5x + 8y - 6z = 14 3x + 4y - 2z = 8 x + 2y - 2z = 3 A. {(-4t + 2, 2t + 1/2, t)} B. {(-3t + 1, 5t + 1/3, t)} C. {(2t + -2, t + 1/2, t)} D. {(-2t + 2, 2t + 1/2, t)} 3. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. x - 2y + z = 0 y - 3z = -1 2y + 5z = -2 A. {(-1, -2, 0)} B. {(-2, -1, 0)} C. {(-5, -3, 0)} D. {(-3, 0, 0)} 4. Use Gauss-Jordan elimination to solve the system. -x - y - z = 1 4x + 5y = 0 y - 3z = 0 A. {(14, -10, -3)} B. {(10, -2, -6)} C. {(15, -12, -4)} D. {(11, -13, -4)} 5. Use Cramer's Rule to solve the following system. 2x = 3y + 2 5x = 51 - 4y A. {(8, 2)} B. {(3, -4)} C. {(2, 5)} D. {(7, 4)} 6. Use Cramer's Rule to solve the following system. 12x + 3y = 15 2x - 3y = 13 A. {(2, -3)} B. {(1, 3)} C. {(3, -5)} D. {(1, -7)} 7. Use Cramer's Rule to solve the following system. x + 2y = 3 3x - 4y = 4 A. {(3, 1/5)} B. {(5, 1/3)} C. {(1, 1/2)} D. {(2, 1/2)} 8. Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. w - 2x - y - 3z = -9 w+x-y=0 3w + 4x + z = 6 2x - 2y + z = 3 A. {(-1, 2, 1, 1)} B. {(-2, 2, 0, 1)} C. {(0, 1, 1, 3)} D. {(-1, 2, 1, 1)} 9. Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 3x + 4y + 2z = 3 4x - 2y - 8z = -4 x+y-z=3 A. {(-2, 1, 2)} B. {(-3, 4, -2)} C. {(5, -4, -2)} D. {(-2, 0, -1)} 10. Use Cramer's Rule to solve the following system. 4x - 5y = 17 2x + 3y = 3 A. {(3, -1)} B. {(2, -1)} C. {(3, -7)} D. {(2, 0)} 11. Use Cramer's Rule to solve the following system. 3x - 4y = 4 2x + 2y = 12 A. {(3, 1)} B. {(4, 2)} C. {(5, 1)} D. {(2, 1)} 12. Use Cramer's Rule to solve the following system. x+y= 7 x-y=3 A. {(7, 2)} B. {(8, -2)} C. {(5, 2)} D. {(9, 3)} 13. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. x + y - z = -2 2x - y + z = 5 -x + 2y + 2z = 1 A. {(0, -1, -2)} B. {(2, 0, 2)} C. {(1, -1, 2)} D. {(4, -1, 3)} 14. Use Gaussian elimination to find the complete solution to each system. 2x + 3y - 5z = 15 x + 2y - z = 4 A. {(6t + 28, -7t - 6, t)} B. {(7t + 18, -3t - 7, t)} C. {(7t + 19, -1t - 9, t)} D. {(4t + 29, -3t - 2, t)} 15. Use Gaussian elimination to find the complete solution to each system. x1 + 4x2 + 3x3 - 6x4 = 5 x1 + 3x2 + x3 - 4x4 = 3 2x1 + 8x2 + 7x3 - 5x4 = 11 2x1 + 5x2 - 6x4 = 4 A. {(-47t + 4, 12t, 7t + 1, t)} B. {(-37t + 2, 16t, -7t + 1, t)} C. {(-35t + 3, 16t, -6t + 1, t)} D. {(-27t + 2, 17t, -7t + 1, t)} 16. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. 3x1 + 5x2 - 8x3 + 5x4 = -8 x1 + 2x2 - 3x3 + x4 = -7 2x1 + 3x2 - 7x3 + 3x4 = -11 4x1 + 8x2 - 10x3+ 7x4 = -10 A. {(1, -5, 3, 4)} B. {(2, -1, 3, 5)} C. {(1, 2, 3, 3)} D. {(2, -2, 3, 4)} 17. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. 2x - y - z = 4 x + y - 5z = -4 x - 2y = 4 A. {(2, -1, 1)} B. {(-2, -3, 0)} C. {(3, -1, 2)} D. {(3, -1, 0)} 18. Use Cramer's Rule to solve the following system. 4x - 5y - 6z = -1 x - 2y - 5z = -12 2x - y = 7 A. {(2, -3, 4)} B. {(5, -7, 4)} C. {(3, -3, 3)} D. {(1, -3, 5)} 19. Give the order of the following matrix; if A = [aij], identify a32 and a23. 1 -5 e 0 7 -6 - -2 1/2 11 -1/5 A. 3 * 4; a32 = 1/45; a23 = 6 B. 3 * 4; a32 = 1/2; a23 = -6 C. 3 * 2; a32 = 1/3; a23 = -5 D. 2 * 3; a32 = 1/4; a23 = 4 20. Find the products AB and BA to determine whether B is the multiplicative inverse of A. 0 1 0 A= 0 0 1 1 0 0 0 0 1 B= 1 0 0 0 1 0 A. AB = I; BA = I3; B = A B. AB = I3; BA = I3; B = A-1 C. AB = I; AB = I3; B = A-1 D. AB = I3; BA = I3; A = B-1 21. Find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: (0, -3), (0, 3) Vertices: (0, -1), (0, 1) A. y2 - x2/4 = 0 B. y2 - x2/8 = 1 C. y2 - x2/3 = 1 D. y2 - x2/2 = 0 22. Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis vertical with length = 10 Length of minor axis = 4 Center: (-2, 3) A. (x + 2)2/4 + (y - 3)2/25 = 1 B. (x + 4)2/4 + (y - 2)2/25 = 1 C. (x + 3)2/4 + (y - 2)2/25 = 1 D. (x + 5)2/4 + (y - 2)2/25 = 1 23. Convert each equation to standard form by completing the square on x and y. 4x2 + y2 + 16x - 6y - 39 = 0 A. (x + 2)2/4 + (y - 3)2/39 = 1 B. (x + 2)2/39 + (y - 4)2/64 = 1 C. (x + 2)2/16 + (y - 3)2/64 = 1 D. (x + 2)2/6 + (y - 3)2/4 = 1 24. Find the standard form of the equation of each hyperbola satisfying the given conditions. Endpoints of transverse axis: (0, -6), (0, 6) Asymptote: y = 2x A. y2/6 - x2/9 = 1 B. y2/36 - x2/9 = 1 C. y2/37 - x2/27 = 1 D. y2/9 - x2/6 = 1 25. Find the focus and directrix of each parabola with the given equation. x2 = -4y A. Focus: (0, -1), directrix: y = 1 B. Focus: (0, -2), directrix: y = 1 C. Focus: (0, -4), directrix: y = 1 D. Focus: (0, -1), directrix: y = 2 26. Find the vertex, focus, and directrix of each parabola with the given equation. (y + 1)2 = -8x A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2 B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3 C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1 D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5 27. Convert each equation to standard form by completing the square on x or y. Then nd the vertex, focus, and directrix of the parabola. y2 - 2y + 12x - 35 = 0 A. (y - 2)2 = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9 B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6 C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6 D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8 28. Convert each equation to standard form by completing the square on x or y. Then nd the vertex, focus, and directrix of the parabola. x2 - 2x - 4y + 9 = 0 A. (x - 4)2 = 4(y - 2); vertex: (1, 4); focus: (1, 3) ; directrix: y = 1 B. (x - 2)2 = 4(y - 3); vertex: (1, 2); focus: (1, 3) ; directrix: y = 3 C. (x - 1)2 = 4(y - 2); vertex: (1, 2); focus: (1, 3) ; directrix: y = 1 D. (x - 1)2 = 2(y - 2); vertex: (1, 3); focus: (1, 2) ; directrix: y = 5 29. Find the standard form of the equation of the following ellipse satisfying the given conditions. Foci: (-2, 0), (2, 0) Y-intercepts: -3 and 3 A. x2/23 + y2/6 = 1 B. x2/24 + y2/2 = 1 C. x2/13 + y2/9 = 1 D. x2/28 + y2/19 = 1 30. Locate the foci and find the equations of the asymptotes. x2/9 - y2/25 = 1 A. Foci: ({36, 0) ;asymptotes: y = 5/3x B. Foci: ({38, 0) ;asymptotes: y = 5/3x C. Foci: ({34, 0) ;asymptotes: y = 5/3x D. Foci: ({54, 0) ;asymptotes: y = 6/3x 31. Find the vertex, focus, and directrix of each parabola with the given equation. (x - 2)2 = 8(y - 1) A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1 B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1 C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1 D. Vertex: (2, 3); focus: (4, 3); directrix: y = -1 32. Find the standard form of the equation of the following ellipse satisfying the given conditions. Foci: (0, -4), (0, 4) Vertices: (0, -7), (0, 7) A. x2/43 + y2/28 = 1 B. x2/33 + y2/49 = 1 C. x2/53 + y2/21 = 1 D. x2/13 + y2/39 = 1 33. Find the solution set for each system by finding points of intersection. x2 + y2 = 1 x2 + 9y = 9 A. {(0, -2), (0, 4)} B. {(0, -2), (0, 1)} C. {(0, -3), (0, 1)} D. {(0, -1), (0, 1)} 34. Locate the foci of the ellipse of the following equation. 25x2 + 4y2 = 100 A. Foci at (1, -11) and (1, 11) B. Foci at (0, -25) and (0, 25) C. Foci at (0, -22) and (0, 22) D. Foci at (0, -21) and (0, 21) 35. Find the focus and directrix of the parabola with the given equation. 8x2 + 4y = 0 A. Focus: (0, -1/4); directrix: y = 1/4 B. Focus: (0, -1/6); directrix: y = 1/6 C. Focus: (0, -1/8); directrix: y = 1/8 D. Focus: (0, -1/2); directrix: y = 1/2 36. Locate the foci and find the equations of the asymptotes. x2/100 - y2/64 = 1 A. Foci: ({= 221, 0); asymptotes: y = 2/5x B. Foci: ({= 231, 0); asymptotes: y = 4/7x C. Foci: ({= 241, 0); asymptotes: y = 4/7x D. Foci: ({= 241, 0); asymptotes: y = 4/5x 1. Use Cramer's Rule to solve the following system. x+y+z=0 2x - y + z = -1 -x + 3y - z = -8 A. {(-1, -3, 7)} B. {(-6, -2, 4)} C. {(-5, -2, 7)} D. {(-4, -1, 7)} 2. Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 5x + 8y - 6z = 14 3x + 4y - 2z = 8 x + 2y - 2z = 3 A. {(-4t + 2, 2t + 1/2, t)} B. {(-3t + 1, 5t + 1/3, t)} C. {(2t + -2, t + 1/2, t)} D. {(-2t + 2, 2t + 1/2, t)} 3. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. x - 2y + z = 0 y - 3z = -1 2y + 5z = -2 A. {(-1, -2, 0)} B. {(-2, -1, 0)} C. {(-5, -3, 0)} D. {(-3, 0, 0)} 4. Use Gauss-Jordan elimination to solve the system. -x - y - z = 1 4x + 5y = 0 y - 3z = 0 A. {(14, -10, -3)} B. {(10, -2, -6)} C. {(15, -12, -4)} D. {(11, -13, -4)} 5. Use Cramer's Rule to solve the following system. 2x = 3y + 2 5x = 51 - 4y A. {(8, 2)} B. {(3, -4)} C. {(2, 5)} D. {(7, 4)} 6. Use Cramer's Rule to solve the following system. 12x + 3y = 15 2x - 3y = 13 A. {(2, -3)} B. {(1, 3)} C. {(3, -5)} D. {(1, -7)} 7. Use Cramer's Rule to solve the following system. x + 2y = 3 3x - 4y = 4 A. {(3, 1/5)} B. {(5, 1/3)} C. {(1, 1/2)} D. {(2, 1/2)} 8. Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. w - 2x - y - 3z = -9 w+x-y=0 3w + 4x + z = 6 2x - 2y + z = 3 A. {(-1, 2, 1, 1)} B. {(-2, 2, 0, 1)} C. {(0, 1, 1, 3)} D. {(-1, 2, 1, 1)} 9. Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 3x + 4y + 2z = 3 4x - 2y - 8z = -4 x+y-z=3 A. {(-2, 1, 2)} B. {(-3, 4, -2)} C. {(5, -4, -2)} D. {(-2, 0, -1)} 10. Use Cramer's Rule to solve the following system. 4x - 5y = 17 2x + 3y = 3 A. {(3, -1)} B. {(2, -1)} C. {(3, -7)} D. {(2, 0)} 11. Use Cramer's Rule to solve the following system. 3x - 4y = 4 2x + 2y = 12 A. {(3, 1)} B. {(4, 2)} C. {(5, 1)} D. {(2, 1)} 12. Use Cramer's Rule to solve the following system. x+y= 7 x-y=3 A. {(7, 2)} B. {(8, -2)} C. {(5, 2)} D. {(9, 3)} 13. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. x + y - z = -2 2x - y + z = 5 -x + 2y + 2z = 1 A. {(0, -1, -2)} B. {(2, 0, 2)} C. {(1, -1, 2)} D. {(4, -1, 3)} 14. Use Gaussian elimination to find the complete solution to each system. 2x + 3y - 5z = 15 x + 2y - z = 4 A. {(6t + 28, -7t - 6, t)} B. {(7t + 18, -3t - 7, t)} C. {(7t + 19, -1t - 9, t)} D. {(4t + 29, -3t - 2, t)} 15. Use Gaussian elimination to find the complete solution to each system. x1 + 4x2 + 3x3 - 6x4 = 5 x1 + 3x2 + x3 - 4x4 = 3 2x1 + 8x2 + 7x3 - 5x4 = 11 2x1 + 5x2 - 6x4 = 4 A. {(-47t + 4, 12t, 7t + 1, t)} B. {(-37t + 2, 16t, -7t + 1, t)} C. {(-35t + 3, 16t, -6t + 1, t)} D. {(-27t + 2, 17t, -7t + 1, t)} 16. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. 3x1 + 5x2 - 8x3 + 5x4 = -8 x1 + 2x2 - 3x3 + x4 = -7 2x1 + 3x2 - 7x3 + 3x4 = -11 4x1 + 8x2 - 10x3+ 7x4 = -10 A. {(1, -5, 3, 4)} B. {(2, -1, 3, 5)} C. {(1, 2, 3, 3)} D. {(2, -2, 3, 4)} 17. Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. 2x - y - z = 4 x + y - 5z = -4 x - 2y = 4 A. {(2, -1, 1)} B. {(-2, -3, 0)} C. {(3, -1, 2)} D. {(3, -1, 0)} 18. Use Cramer's Rule to solve the following system. 4x - 5y - 6z = -1 x - 2y - 5z = -12 2x - y = 7 A. {(2, -3, 4)} B. {(5, -7, 4)} C. {(3, -3, 3)} D. {(1, -3, 5)} 19. Give the order of the following matrix; if A = [aij], identify a32 and a23. 1 -5 e 0 7 -6 - -2 1/2 11 -1/5 A. 3 * 4; a32 = 1/45; a23 = 6 B. 3 * 4; a32 = 1/2; a23 = -6 C. 3 * 2; a32 = 1/3; a23 = -5 D. 2 * 3; a32 = 1/4; a23 = 4 20. Find the products AB and BA to determine whether B is the multiplicative inverse of A. 0 1 0 A= 0 0 1 1 0 0 0 0 1 B= 1 0 0 0 1 0 A. AB = I; BA = I3; B = A B. AB = I3; BA = I3; B = A-1 C. AB = I; AB = I3; B = A-1 D. AB = I3; BA = I3; A = B-1 21. Find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: (0, -3), (0, 3) Vertices: (0, -1), (0, 1) A. y2 - x2/4 = 0 B. y2 - x2/8 = 1 C. y2 - x2/3 = 1 D. y2 - x2/2 = 0 22. Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis vertical with length = 10 Length of minor axis = 4 Center: (-2, 3) A. (x + 2)2/4 + (y - 3)2/25 = 1 B. (x + 4)2/4 + (y - 2)2/25 = 1 C. (x + 3)2/4 + (y - 2)2/25 = 1 D. (x + 5)2/4 + (y - 2)2/25 = 1 23. Convert each equation to standard form by completing the square on x and y. 4x2 + y2 + 16x - 6y - 39 = 0 A. (x + 2)2/4 + (y - 3)2/39 = 1 B. (x + 2)2/39 + (y - 4)2/64 = 1 C. (x + 2)2/16 + (y - 3)2/64 = 1 D. (x + 2)2/6 + (y - 3)2/4 = 1 24. Find the standard form of the equation of each hyperbola satisfying the given conditions. Endpoints of transverse axis: (0, -6), (0, 6) Asymptote: y = 2x A. y2/6 - x2/9 = 1 B. y2/36 - x2/9 = 1 C. y2/37 - x2/27 = 1 D. y2/9 - x2/6 = 1 25. Find the focus and directrix of each parabola with the given equation. x2 = -4y A. Focus: (0, -1), directrix: y = 1 B. Focus: (0, -2), directrix: y = 1 C. Focus: (0, -4), directrix: y = 1 D. Focus: (0, -1), directrix: y = 2 26. Find the vertex, focus, and directrix of each parabola with the given equation. (y + 1)2 = -8x A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2 B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3 C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1 D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5 27. Convert each equation to standard form by completing the square on x or y. Then nd the vertex, focus, and directrix of the parabola. y2 - 2y + 12x - 35 = 0 A. (y - 2)2 = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9 B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6 C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6 D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8 28. Convert each equation to standard form by completing the square on x or y. Then nd the vertex, focus, and directrix of the parabola. x2 - 2x - 4y + 9 = 0 A. (x - 4)2 = 4(y - 2); vertex: (1, 4); focus: (1, 3) ; directrix: y = 1 B. (x - 2)2 = 4(y - 3); vertex: (1, 2); focus: (1, 3) ; directrix: y = 3 C. (x - 1)2 = 4(y - 2); vertex: (1, 2); focus: (1, 3) ; directrix: y = 1 D. (x - 1)2 = 2(y - 2); vertex: (1, 3); focus: (1, 2) ; directrix: y = 5 29. Find the standard form of the equation of the following ellipse satisfying the given conditions. Foci: (-2, 0), (2, 0) Y-intercepts: -3 and 3 A. x2/23 + y2/6 = 1 B. x2/24 + y2/2 = 1 C. x2/13 + y2/9 = 1 D. x2/28 + y2/19 = 1 30. Locate the foci and find the equations of the asymptotes. x2/9 - y2/25 = 1 A. Foci: ({36, 0) ;asymptotes: y = 5/3x B. Foci: ({38, 0) ;asymptotes: y = 5/3x C. Foci: ({34, 0) ;asymptotes: y = 5/3x D. Foci: ({54, 0) ;asymptotes: y = 6/3x 31. Find the vertex, focus, and directrix of each parabola with the given equation. (x - 2)2 = 8(y - 1) A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1 B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1 C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1 D. Vertex: (2, 3); focus: (4, 3); directrix: y = -1 32. Find the standard form of the equation of the following ellipse satisfying the given conditions. Foci: (0, -4), (0, 4) Vertices: (0, -7), (0, 7) A. x2/43 + y2/28 = 1 B. x2/33 + y2/49 = 1 C. x2/53 + y2/21 = 1 D. x2/13 + y2/39 = 1 33. Find the solution set for each system by finding points of intersection. x2 + y2 = 1 x2 + 9y = 9 A. {(0, -2), (0, 4)} B. {(0, -2), (0, 1)} C. {(0, -3), (0, 1)} D. {(0, -1), (0, 1)} 34. Locate the foci of the ellipse of the following equation. 25x2 + 4y2 = 100 A. Foci at (1, -11) and (1, 11) B. Foci at (0, -25) and (0, 25) C. Foci at (0, -22) and (0, 22) D. Foci at (0, -21) and (0, 21) 35. Find the focus and directrix of the parabola with the given equation. 8x2 + 4y = 0 A. Focus: (0, -1/4); directrix: y = 1/4 B. Focus: (0, -1/6); directrix: y = 1/6 C. Focus: (0, -1/8); directrix: y = 1/8 D. Focus: (0, -1/2); directrix: y = 1/2 36. Locate the foci and find the equations of the asymptotes. x2/100 - y2/64 = 1 A. Foci: ({= 221, 0); asymptotes: y = 2/5x B. Foci: ({= 231, 0); asymptotes: y = 4/7x C. Foci: ({= 241, 0); asymptotes: y = 4/7x D. Foci: ({= 241, 0); asymptotes: y = 4/5x