Proof Let A be a nonsingular matrix of order 3. Provethat if {v1, v2, v3} is a linearly

Chapter 4, Problem 75

(choose chapter or problem)

Let A be a nonsingular matrix of order 3. Prove that if \(\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}\) is a linearly independent set in \(M_{3.1}\), then the set \(\left\{A \mathbf{v}_{1}, A \mathbf{v}_{2}, A \mathbf{v}_{3}\right\}\) is also linearly independent. Explain, by means of an example, why this is not true when A is singular.

Text Transcription:

{mathbf v_1, mathbf v_2, mathbf v_3}

M_3.1

{A mathbf v_1, A mathbf v_2, A mathbf v_3}