A First Course in Linear Algebra · Problem M31

Representations — Robert Beezer

Mathematics — Linear Algebra · inverse-linear-transformation

Problem

The linear transformation

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

is invertible. 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}