Solved: Diagonal Matrix for a Linear Transformation In

Chapter 6, Problem 23

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In Exercises 23 and 24, let A be the matrix for \(T: R^{3} \rightarrow R^{3}\) relative to the standard basis. Find the diagonal matrix A’ for T relative to the basis B’.

\(\begin{array}{l} A=\left[\begin{array}{rrr} 0 & 2 & 0 \\ 1 & -1 & 0 \\ 0 & 0 & 1 \end{array}\right] \\ B^{\prime}=\{(-1,1,0),(2,1,0),(0,0,1)\} \end{array} \)

Text Transcription:

T: R^3 rightarrow R^3

A = [_0^1^0 _0^-1^2 _1^0^0], B’ = [(-1,1,0), (2,1,0), (0,0,1)}