A First Course in Linear Algebra · Problem MR.C41

Representations — Robert Beezer

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

Problem

Prove that the linear transformation

S

is invertible. Then find a formula for the inverse linear transformation,

S^{-1}

, by employing a matrix inverse.

S: P_1 \to M_{12}, \quad S(a+bx) = \begin{bmatrix}3a+b & 2a+b\end{bmatrix}