Consider $T:\mathbb{R^3}\rightarrow \mathbb{R^3}$ a linear transformation with matricial representation (in the canonical basis of $\mathbb{R^3}$:
$A = \begin{bmatrix} 1 & 0 & 0 \\[0.3em] 0 & 1 & 2 \\[0.3em] 0 & 0 & 1 \end{bmatrix}$
Find the matrix that represents $T$ in the respect to the basis $b=<(1,1,1), (1,1,0), (1,0,0)$
so i'm not understanding how to do this...
I tried to calculate the changing basis matrix (from the canonical basis to the basis we want). But now what to I do with that matrix? I thought in might be useful but the fact that we are trying to calculate the transformation in another basis is making me confused :/
By the way the matrix of changing basis that i reached to was:
$B = \begin{bmatrix} 1 & 1 & 1 \\[0.3em] 1 & 1 & 0 \\[0.3em] 1 & 0 & 0 \end{bmatrix}$
Can someone clarify to me how should I proceed?
Thank you very much!
Your matrix should look like $$T=BA(B)^{-1}$$
It's the general formula.