A First Course in Linear Algebra · Problem MR.C42

Representations — Robert Beezer

Mathematics — Linear Algebra · invertible-linear-transformation-matrix-representation

Problem

The linear transformation

R: M_{12} \to M_{21}

is invertible. Use a matrix representation to determine a formula for the inverse linear transformation

R^{-1}: M_{21} \to M_{12}

R\left(\begin{bmatrix}a & b\end{bmatrix}\right) = \begin{bmatrix}a+3b\\ 4a+11b\end{bmatrix}