10.3 & 10.4

1.

Find the value at the determinant. 3 1 -4 1 -3 5 1 4 1 The value at the determinant is D. Solve the system of equations using Cramer's Rule if it is applicable. x+ y - z= 4 (1) 3x - y + 2z = -5 (2) x + 3y - 2z = 5 (3) Select the correct choice below and fill in any answer boxes within your choice. O A. Cramer's Rule is applicable. The solution is x = V = and z = (Simplify your answers.) O B. Cramer's Rule is not applicable.Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. x + 4}; + 32 = 4 2x 3}; + 52 = 2 4x 16y 122 = 16 Select the correct choice below and, if necessary. ll in the answer boxes to complete your choice. Cl A- Cramer's rule is applicable. The solution is x = i y: ,2: (Simplify.f your answers.) if] B. Cramer's Rule is not applicable. Determine whether 6A + 5B is defined. If it is defined, express the result as a single matrix; if it is not, say "not defined." 0 2 -5 2 1 0 A= B= 1 6 -5 4 -3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The expression 6A + 5B is defined. 6A + 5B = O B. The expression 6A + 5B is not defined.Determine whether AC is defined. If it is defined, express the result as a single matrix; if it is not, say "not defined." 2 1 0 5 -6 3 1 0 A = B = L C= 3 4 1 4 1 -2 2 -2 - 3 5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The expression AC is defined. AC = O B. The expression AC is not defined.Determine whether CA is defined. If it is defined, express the result as a single matrix; if it is not, say "not defined." 3 1 0 6 -6 6 1 0 A= B = 1 3 3 - 3 , C= 6 4 -2 3 -3 - 5 6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The expression CA is defined. CA = O B. The expression CA is not defined.Determine whether the product is defined. If it is defined, find the product; if it is not, say "not defined." 2 - 2 2 151 0 2 -1 1 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. 2 -2 2 1 5 1 The product is defined. 2 -1 1 1 O B. The product is not defined.Determine whether the product is defined. If it is defined: find the product; if it ie not, so}; "net defined." 10112 15161 281?1 Select the correct choice below and, if necessary: fill in the answer box to complete your choice. 9211A. 1 o 1 1 2 The product is defined. 1 5 1 B 1 2 6 1 f 1 {'1 B. The product is not defined. Find the inverse of the given nonsingular matrix. 8 7 4 4 8 7 The inverse of the matrix is 4 4 (Type an integer or simplified fraction for each matrix element.)Find the inverse of the given nonsingular matrix. 1 - 1 0 2 -1 -8 -9 0 1 - 1 1 The inverse of the matrix 0 2 -1 is -8 -9 0 (Type an integer or simplified fraction for each matrix element.)Use the given inverse to solve the system of equations. 6x + 5y = 6 5 The inverse of is - 2x - 2y = -2 -2 -2 - 1 - 3 X= y=1 - 1 1 8 - 8 The inverse of 0 -2 1 is - 7 7 -1 . Use it to solve the following system of equations. -7 -80 - 14 15 -2 X - y+ z= 0 - 2y + z= 1 -7x - By = 4 X= y = Z= (Simplify your answers.)Algebraically solve the system of equations using any method you wish. X - 2y + 4z = 1 - 3x + 5y - 2z = 27 5x - 4y = - 35 Select the correct choice below and fill in any answer boxes within your choice. O A. The solution is . (Simplify your answers.) O B. There are infinitely many solutions. Using ordered triplets, the solution can be written as { (x,y, z) | x = by = any real number} (Simplify your answers. Type expressions using z as the variable as needed. Do not factor.) O C. There are infinitely many solutions. Using ordered triplets, the solution can be written as (x, y, z ) x = y any real number, z any real number} (Simplify your answer. Type an expression using y and z as the variables as needed. Do not factor.) O D. There is no solution.Form a polynomial whose zeros and degree are given. Zeros: 2, multiplicity 1; 3, multiplicity 2; degree 3 Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below. f(x) = (Simplify your answer.)