Standard matrix of a transformation, matrix representation [on hold]
-1
I know that the answer is $left[begin{matrix} 2 & -1 \ 1 & 1 end{matrix}right]$ , but how to get the answer? Let $mathcal{B} = { mathbf{b}_1 , mathbf{b}_2 }$ be the basis for $mathbb{R}^2$ with $mathbf{b}_1 = left [ begin{matrix} 1 \ 1 end{matrix} right ]$ , $mathbf{b}_2 = left [ begin{matrix} 0 \ 1 end{matrix} right ]$ . Furthermore, let $T: mathbb{R}^2 to mathbb{R}^2$ be a linear transformation. The matrix representation of $T$ with respect to $mathcal{B}$ is $[T]_mathcal{B} = left [ begin{matrix} 1 & -1 \ 1 & 2 end{matrix} right ]$ . What is the standard matrix of $T$ ? Original problem:
linear-algebra matrices transformation
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