Chapter 6.4, Problem 24E

Diagonal Matrix for a Linear Transformation In Exercises 23 and 24, let $A$be the matrix for $T:R^3\to R^3$relative to the standard basis. Find diagonal matrix $A^{\prime }$for $T$relative to the basis $B^{\prime }$.

$A=\left[\begin{array}{ccc}\frac{3}{2}& -1& -\frac{1}{2}\\ -\frac{1}{2}& 2& \frac{1}{2}\\ \frac{1}{2}& 1& \frac{5}{2}\end{array}\right]$

$B^{\prime }=\left\{\left(1,1,-1\right),\left(1,-1,1\right),\left(-1,1,1\right)\right\}$