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
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 point) If A and B are 3 x 3 matrices, det(A) = -5, det(B) = 9, then det(AB) = det(-2A) = det(AT) = det(B-1) = det(B3) =
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. 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...
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...
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...
Let A and B be n × m, and m × n matrices over F respectively. Prove that rn ) = det(In-AB) = det(I,n-BA). In det A Let A and B be n × m, and m × n matrices over F respectively. Prove that rn ) = det(In-AB) = det(I,n-BA). In det A
[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)
Problem 5. Let n N. The goal of this problem is to show that if two real n x n matrices are similar over C, then they are also similar over IK (a) Prove that for all X, y є Rnxn, the function f(t) det (X + ty) is a polynomial in t. (b) Prove that if X and Y are real n × n matrices such that X + ừ is an invertible complex matrix, then there exists a...
Matrices multiplication and Partitioned multiplication: matrix X= 2 1 5 4 2 3 Matrix Y= 1 2 4 2 3 1 1. Find the XY^(T) T means transpose 2.Compute the outer product expansion of XY^(T) . 3. did you get the same answer from 1 and 2?