Explain why the columns of an n × n matrix A span n when A

Chapter 2, Problem 22E

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QUESTION:

Explain why the columns of an \(n \times n\) matrix A span \(\mathbb{R}^{n}\) when A is invertible. [Hint: Review Theorem 4 in Section 1.4.]

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QUESTION:

Explain why the columns of an \(n \times n\) matrix A span \(\mathbb{R}^{n}\) when A is invertible. [Hint: Review Theorem 4 in Section 1.4.]

ANSWER:

Solution: Step1: We have to explain why the columns of an n × n matrix A span n when A is invertible.

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