A First Course in Linear Algebra · Problem MR.C40

Representations — Robert Beezer

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

Problem

Let

S_{22}

be the set of

2\times 2

symmetric matrices. Verify that the linear transformation

R

is invertible and find

R^{-1}

R: S_{22} \to P_2, \quad R\left(\begin{bmatrix}a&b\\b&c\end{bmatrix}\right) = (a-b)+(2a-3b-2c)x+(a-b+c)x^2