Let A be a 3 x 3 matrix with det(A) = 0. Determine if each of the following statements is true or false. (a) Ax = 0 has a trivial solution. (b) For every b, Ax = b has at least one solution. (c) For every matrix B, we have det(AB) = 0. (d) For every matrix B, we have det(A + B) = det(B).
Let A be a 3 x 3 matrix with det(A) = 0. Determine if each of the following statements is true or false. (a) Ax = 0 has a trivial solution. (b) For every b, Ax = b has at least one solution. (c) For every matrix B, we have det(AB) = 0. (d) For every matrix B, we have det(A + B) = det(B).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 63EQ
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Let A be a 3 x 3 matrix with det(A) = 0. Determine if each of the following statements is true or false.
(a) Ax = 0 has a trivial solution.
(b) For every b, Ax = b has at least one solution.
(c) For every matrix B, we have det(AB) = 0.
(d) For every matrix B, we have det(A + B) = det(B).
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