Linear Algebra and Its Applications · Problem 2.4.25

Vector Spaces — Gilbert Strang

Mathematics · four-fundamental-subspaces

Problem

Which subspaces are the same for these matrices of different sizes? (a)

\begin{bmatrix} A \end{bmatrix}

and

\begin{bmatrix} A \\ A \end{bmatrix}

. (b)

\begin{bmatrix} A \\ A \end{bmatrix}

and

\begin{bmatrix} A & A \\ A & A \end{bmatrix}

. Prove that all three matrices have the same rank

r