Exercise7

Provide a justification for your response to the following questions.

  1. Suppose that \(A\) is a square matrix with two identical columns. Can \(A\) be invertible?

  2. Suppose that \(A\) is a square matrix with two identical rows. Can \(A\) be invertible?

  3. Suppose that \(A\) is an invertible matrix and that \(AB = AC\text{.}\) Can you conclude that \(B = C\text{?}\)

  4. Suppose that \(A\) is an invertible \(n\times n\) matrix. What can you say about the span of the columns of \(A^{-1}\text{?}\)

  5. Suppose that \(A\) is an invertible matrix and that \(B\) is row equivalent to \(A\text{.}\) Can you guarantee that \(B\) is invertible?

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