Question 4.1.9: Let T: R³→ R³ be a linear operator and B a basis for R³ give...
Let T: R³→ R³ be a linear operator and B a basis for R³ given by
B= \left\{\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix},\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix},\begin{bmatrix} 1 \\ 1 \\ 2 \end{bmatrix} \right\}
If
T\left(\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}\right) = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \quad T\left(\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}\right) = \begin{bmatrix} -1 \\ -2 \\ -3 \end{bmatrix} \quad T\left(\begin{bmatrix} 1 \\ 1 \\ 2 \end{bmatrix}\right) = \begin{bmatrix} 2 \\ 2 \\ 4 \end{bmatrix}
find
T\left(\begin{bmatrix} 2 \\ 3 \\ 6 \end{bmatrix}\right)
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