Let $T:R^3 \rightarrow R^3$ be a non-invertible linear transformation that's represented with respect to the base: $ B = ((1,0,1),(0,1,-1),(1,-1,0))$
By the matrix:
$$[T]_B=\begin{pmatrix} 1 & 0 & 1 \\ 1 & \alpha & 2\alpha \\ \alpha & 1 & 2\alpha \end{pmatrix}$$
I want to find $\alpha$ and the matrix that represent $T$ with respect to the standard basis.
I'm not sure how to begin with this exercise, can someone guide me please? I don't know what is the procedure of finding $\alpha$