If A, B are 3 x 3 matrices such that det(AB-1) = 12 and det(A) = 4. Find 1) det(B) 2) det(AT. (3B)-1) 3) If A? + AB = { 1, find det(A + B)
1. (10 points) Let A and B be 3 x 3 matrices, with det A = -3 and det B = 2. Compute (a) det AB (6) det B4 (c) det 3B (d) det A"B" AT (e) det B-AB
[4 points Suppose A, B, and Care 5 x 5 matrices with det(A) = -2, det(B) = 10 and the columns of C are linearly dependent. Find the following or state that there is not enough information: (a) det(10B-) (b) det(AB) (c) det(CA+CB)
Let A and B be 3x3 matrices, with det A=9 and det B = - 6. Use properties of determinants to complete parts (a) through (e) below. a. Compute det AB. det AB = (Type an integer or a fraction.) b. Compute det 5A. det 5A = (Type an integer or a fraction.) c. Compute det BT. det BT = (Type an integer or a fraction.) d. Compute det A-7. - 1 det A (Type an integer or a simplified...
4. Let A and B be 4 x 4 matrices. Suppose det A= 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(AT)? (d) (4 points) What is det(A-1)? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of AT are linearly independent. [2] and us 6. (6 points) Let vi...
X and Y are n x n matrices and det X^T = 3 and B^-1 = 2 T F det(X^2 Y^2 (X^-1)^T) = 12 T F detX/(detY^T) = 6 T F det(X^3 Y) = 27/2 T F det(X^-1 Y^2 X ^T) = -4 T F det(X^-1 B^T) = 6 T F det(XY) = 3/2
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det (A?)? (d) (4 points) What is det(A-?)? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of AT are linearly independent. and 2 6. (6 points) Let...
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(AT)? (d) (4 points) What is det(A-')? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of A™ are linearly independent. and t = [ ] 6. (6...
(1 point) If det b 1 3 and det b 2 e 3 then a 5 det|b 5 el=15 and c 5 f c 8 f (1 point) If det b 1 3 and det b 2 e 3 then a 5 det|b 5 el=15 and c 5 f c 8 f
a. Compute det \(\mathrm{AB}\).det \(\mathrm{AB}=\square\) (Type an integer or a fraction.)b. Compute det \(5 \mathrm{~A}\).det \(5 \mathrm{~A}=\square\) (Type an integer or a fraction.)c. Compute det \(\mathrm{B}^{\top}\).\(\operatorname{det} \mathrm{B}^{\top}=\square\) (Type an integer or a fraction.)d. Compute \(\operatorname{det} A^{-1}\).\(\operatorname{det} \mathrm{A}^{-1}=\square\) (Type an integer or a simplified fraction.)e. Compute det \(\mathrm{A}^{3}\).det \(\mathrm{A}^{3}=\square\) (Type an integer or a fraction.)