Solution: Stacked matrix. Let A be an m * n matrix, and consider the stacked matrix S defined by
Question: Stacked matrix. Let \(A\) be an \(m \times n\) matrix, and consider the stacked matrix \(S\) defined by
\[S=\left[\begin{array}{c} A \\ I \end{array}\right]\]When does \(S\) have linearly independent columns? When does \(S\) have linearly independent rows? Your answer can depend on m, n, or whether or not \(A\) has linearly independent columns or rows.
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