# Finding the matrix for a linear transformation on a vector space when the basis changes

Let B={$u_1,u_2,u_3$} as basis of Vector Space V, and Let T: V→V be the linear operator defined by,
$$[T]_B=\begin{bmatrix} -3 & 4 & 7 \\ 1 & 0 & -2 \\ 0 & 1 & 0 \\ \end{bmatrix}$$ Find $[T]_{B'}$. B'={$v_1,v_2,v_3$} is basis of V defined by $v_1 = u_1, v_2 = u_1 + u_2, v_3 = u_1 + u_2 + u_3$.

I have solved questions by my effort, but I'm not sure for this answer. Please check and give me a hint for this question. Thank you.