We know that det(A) can be calculated as ad-bc.
Problem 8. a) Find the determinant det (A) for the matrix [1 -3 41 A 2 0 -1 1 b) Decide whether the matrix A has an inverse. If the inverse matrix A-1 exists, find its determinant det(A-1).
(1 point) Compute the determinant of the matrix -1 -2 -4 -6 -7 -7 7 7 A= 0 0 0 0 -4 -5 7 det(A) (1 point) Find the determinant of the matrix 6 A- 6 -9 -7 det(A) (1 point) Find the determinant of the matrix 2 2 -2 B= 1 -1 2 3 -2 det (B)
(10 pts) If the determinant of a 5 x 5 matrix A is det (A) = 8, and the matrix B is obtained from A by multiplying the second column by 9, then det (B) =
(1 point) Find the determinant of the matrix [1 0 0 -2] M-1 0 3 0 To 3 0 Lo 1 -3 2 o det(M) =
(16). Determine the determinant of the following n x n matrix: 2 3 II 2 3 0 3 00 9 (17). If A= then A= 9 3 7 2 1 (18). Let A= 1 2 If x= is an eigenvector of A-1, then k = 1 2 (19). Let A € R3x3 and det(A - 1) = det(A + 1) = det(A - 21) = 0. Then det(A) = 1 3 3 2 (20). The rank of matrix A =...
1. Find the determinant of the follow ing matrices 1 8 [2 1 B=3 8 10 det BT
44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove that det ((-A-t +1 where t = Tr(A). 44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove...
9. Given det(A5x5)-3, find det(A3), det(5A), det(2AT), det(3A-1). 9. Given det(A5x5)-3, find det(A3), det(5A), det(2AT), det(3A-1).
(3 points) Let A be a 4 x 4 matrix with det(A) = 8. 1. If the matrix B is obtained from mes the second row to the first, then det(B) = 2. If the matrix C is obtained from A by swapping the first and second rows , then det(C) = 3. If the matrix D is obtained from A by multiplying the first row by 5, then det(D) =
I need to find det (lambda * x - A): The determinant for this answer is: -x^3+7x-6. How can I get this answer? 8. (10 points) Find the general solution to the homogeneous system of DE: 3 2 6 x' = Ax where A = -2 -1 -2 -4) 1 -2