1 of 40 2.5 Points Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 8x + 5y + 11z = 30 -x - 4y + 2z = 3 2x - y + 5z = 12 A. {(3 - 3t, 2 + t, t)} B. {(6 - 3t, 2 + t, t)} C. {(5 - 2t, -2 + t, t)} D. {(2 - 1t, -4 + t, t)} Question 2 of 40 2.5 Points 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)} Question 3 of 40 2.5 Points 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)} Question 4 of 40 2.5 Points 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)} Question 5 of 40 2.5 Points Use Gaussian elimination to find the complete solution to each system. x - 3y + z = 1 -2x + y + 3z = -7 x - 4y + 2z = 0 A. {(2t + 4, t + 1, t)} B. {(2t + 5, t + 2, t)} C. {(1t + 3, t + 2, t)} D. {(3t + 3, t + 1, t)} Question 6 of 40 2.5 Points 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)}. Question 7 of 40 2.5 Points 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)} Question 8 of 40 2.5 Points 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)} Question 9 of 40 2.5 Points 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)} Question 10 of 40 2.5 Points Give the order of the following matrix; if A = [a ij], 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 Question 11 of 40 2.5 Points Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. x + 3y = 0 x+y+z=1 3x - y - z = 11 A. {(3, -1, -1)} B. {(2, -3, -1)} C. {(2, -2, -4)} D. {(2, 0, -1)} Question 12 of 40 Use Cramer's Rule to solve the following system. 2x = 3y + 2 5x = 51 - 4y 2.5 Points A. {(8, 2)} B. {(3, -4)} C. {(2, 5)} D. {(7, 4)} Question 13 of 40 Use Cramer's Rule to solve the following system. 12x + 3y = 15 2x - 3y = 13 A. {(2, -3)} 2.5 Points B. {(1, 3)} C. {(3, -5)} D. {(1, -7)} Question 14 of 40 Use Cramer's Rule to solve the following system. 4x - 5y - 6z = -1 x - 2y - 5z = -12 2x - y = 7 2.5 Points A. {(2, -3, 4)} B. {(5, -7, 4)} C. {(3, -3, 3)} D. {(1, -3, 5)} Question 15 of 40 2.5 Points Find the products AB and BA to determine whether B is the multiplicative inverse of A. 01 0 A= 00 1 1 0 0 00 1 B= 10 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 Question 16 of 40 Use Cramer's Rule to solve the following system. 2.5 Points x + 2y = 3 3x - 4y = 4 A. {(3, 1/5)} B. {(5, 1/3)} C. {(1, 1/2)} D. {(2, 1/2)} Question 17 of 40 If AB = -BA, then A and B are said to be anticommutative. 0 -1 10 Are A = and B = anticommutative? 10 0 -1 A. AB = -AB so they are not anticommutative. 2.5 Points B. AB = BA so they are anticommutative. C. BA = -BA so they are not anticommutative. D. AB = -BA so they are anticommutative. Question 18 of 40 2.5 Points Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 2w + x - y = 3 w - 3x + 2y = -4 3w + x - 3y + z = 1 w + 2x - 4y - z = -2 A. {(1, 3, 2, 1)} B. {(1, 4, 3, -1)} C. {(1, 5, 1, 1)} D. {(-1, 2, -2, 1)} Question 19 of 40 2.5 Points 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)} Question 20 of 40 2.5 Points 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)} Question 21 of 40 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 2.5 Points C. Foci: ({= 241, 0); asymptotes: y = 4/7x D. Foci: ({= 241, 0); asymptotes: y = 4/5x Question 22 of 40 2.5 Points Convert each equation to standard form by completing the square on x or y. Then find 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 Question 23 of 40 2.5 Points Find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: (-4, 0), (4, 0) Vertices: (-3, 0), (3, 0) A. x2/4 - y2/6 = 1 B. x2/6 - y2/7 = 1 C. x2/6 - y2/7 = 1 D. x2/9 - y2/7 = 1 Question 24 of 40 2.5 Points 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 Question 25 of 40 Locate the foci of the ellipse of the following equation. 2.5 Points 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) Question 26 of 40 2.5 Points Locate the foci of the ellipse of the following equation. 7x2 = 35 - 5y2 A. Foci at (0, -2) and (0, 2) B. Foci at (0, -1) and (0, 1) C. Foci at (0, -7) and (0, 7) D. Foci at (0, -5) and (0, 5) Question 27 of 40 2.5 Points Find the vertex, focus, and directrix of each parabola with the given equation. (y + 3)2 = 12(x + 1) A. Vertex: (-1, -3); focus: (1, -3); directrix: x = -3 B. Vertex: (-1, -1); focus: (4, -3); directrix: x = -5 C. Vertex: (-2, -3); focus: (2, -4); directrix: x = -7 D. Vertex: (-1, -3); focus: (2, -3); directrix: x = -4 Question 28 of 40 2.5 Points Find the vertex, focus, and directrix of each parabola with the given equation. (x + 1)2 = -8(y + 1) A. Vertex: (-1, -2); focus: (-1, -2); directrix: y = 1 B. Vertex: (-1, -1); focus: (-1, -3); directrix: y = 1 C. Vertex: (-3, -1); focus: (-2, -3); directrix: y = 1 D. Vertex: (-4, -1); focus: (-2, -3); directrix: y = 1 Question 29 of 40 2.5 Points Find the focus and directrix of each parabola with the given equation. y2 = 4x A. Focus: (2, 0); directrix: x = -1 B. Focus: (3, 0); directrix: x = -1 C. Focus: (5, 0); directrix: x = -1 D. Focus: (1, 0); directrix: x = -1 Question 30 of 40 2.5 Points 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 Question 31 of 40 Locate the foci and find the equations of the asymptotes. 2.5 Points 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 Question 32 of 40 2.5 Points 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 Question 33 of 40 2.5 Points 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 Question 34 of 40 2.5 Points 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 Question 35 of 40 2.5 Points 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)} Question 36 of 40 2.5 Points Find the vertices and locate the foci of each hyperbola with the given equation. y2/4 - x2/1 = 1 A. Vertices at (0, 5) and (0, -5); foci at (0, 14) and (0, -14) B. Vertices at (0, 6) and (0, -6); foci at (0, 13) and (0, -13) C. Vertices at (0, 2) and (0, -2); foci at (0, 5) and (0, -5) D. Vertices at (0, 1) and (0, -1); foci at (0, 12) and (0, -12) Question 37 of 40 Locate the foci of the ellipse of the following equation. x2/16 + y2/4 = 1 A. Foci at (-23, 0) and (23, 0) 2.5 Points B. Foci at (53, 0) and (23, 0) C. Foci at (-23, 0) and (53, 0) D. Foci at (-72, 0) and (52, 0) Question 38 of 40 2.5 Points Convert each equation to standard form by completing the square on x and y. 9x2 + 25y2 - 36x + 50y - 164 = 0 A. (x - 2)2/25 + (y + 1)2/9 = 1 B. (x - 2)2/24 + (y + 1)2/36 = 1 C. (x - 2)2/35 + (y + 1)2/25 = 1 D. (x - 2)2/22 + (y + 1)2/50 = 1 Question 39 of 40 2.5 Points Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of major axis: (7, 9) and (7, 3) Endpoints of minor axis: (5, 6) and (9, 6) A. (x - 7)2/6 + (y - 6)2/7 = 1 B. (x - 7)2/5 + (y - 6)2/6 = 1 C. (x - 7)2/4 + (y - 6)2/9 = 1 D. (x - 5)2/4 + (y - 4)2/9 = 1 Question 40 of 40 Locate the foci and find the equations of the asymptotes. 4y2 - x2 = 1 A. (0, 4/2); asymptotes: y = 1/3x B. (0, 5/2); asymptotes: y = 1/2x C. (0, 5/4); asymptotes: y = 1/3x D. (0, 5/3); asymptotes: y = 1/2x 2.5 Points