Question

Let $T:R^{3}\rightarrow R^{3}$ be a linear transformation defined by $T(a,b,c)=(a+b-c, a+b+c, b-c)$. Then the matrix of $T$ with respect to the ordered basis $B = \{(0,1,0), (0,0,1), (1,0,0)\}$ is}

• A. $\left[\begin{matrix}1& 1&-1\\ 1& 1& 1\\ 0& 1&-1\end{matrix}\right]$
• B. $\left[\begin{matrix}1& 1& 0\\ 1& 1& 1\\ 1& 0&-1\end{matrix}\right]$
• C. $\left[\begin{matrix}1&-1& 1
  1& 1& 1
  1&-1& 0\end{matrix}\right]$
• D. $\left[\begin{matrix}1& 1& 1
  1&-1& 0
  1&-1& 1\end{matrix}\right]$

Hint:

Matrix of $T = [ [T(v_1)]_B | [T(v_2)]_B | [T(v_3)]_B ]$. The columns are images of the basis vectors.

Answer 1

The Correct Option is C