(1 point) Find the determinant of the matrix A= -9 1-8 3 | det(A) =
Find a formula for det(rA) when A is an nxn matrix. Choose the correct answer below. A. det(rA) = det r•A B. det(rA) = rodet A C. det(A) • det A OD. det(rA) = det A
(a) A is a 4 X4 matrix and 5(A + 1) = 1. Enter det (A + 1). (b) A is a 3 x3 matrix and -A +61 = 0. Enter det (A + 1). (c) A is a 2 X2 matrix and A2 + 2 A – 35 I = 0. If det (A + I)> 0, enter det (A + I).
Q1. Suppose that A is an n x n invertible matrix. (a) Show that det(A-1) = (det(A))-. (b) Show that det(APA-1) = det(P) for any n x n matrix P.
(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) =
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).
Matrices A and B are called similar if there exists an invertible Matrix P such that: A= PBP^-1 Show that det(A) = det(B)
(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)
7.(6) Let A be a square matrix of size 4x4 and if det(A) = -1. Find det(3A) and the rank of A.
Linear algebra 6. Prove that if a real matrix An xn satisfies A100-Inxn (the identity matrix), then det(A) ±1. 6. Prove that if a real matrix An xn satisfies A100-Inxn (the identity matrix), then det(A) ±1.