A First Course in Linear Algebra · Problem RQ-LISS-1

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · linear-independence-vector-spaces

Problem

Is the set of matrices below linearly independent or linearly dependent in the vector space

M_{22}

? Why or why not?

\left\{\begin{bmatrix}1 & 3\\-2 & 4\end{bmatrix},\begin{bmatrix}-2 & 3\\3 & -5\end{bmatrix},\begin{bmatrix}0 & 9\\-1 & 3\end{bmatrix}\right\}