Question

If T: R3 -> R3 is a linear transformation such that
T1 [1,0,0] = [-3,2,-2], T2 [0,1,0] = [4,-2,2], and T3 [0,0,1] = [-4,3,1], the T [0,-3,4] =

Answer 1

\(T(\begin{bmatrix}
0 \\
-3 \\
4
\end{bmatrix}) =
\begin{bmatrix}
-3 & 4 & -4 \\
2 & -2 & 3 \\
-2 & 2 & 1
\end{bmatrix}
*\begin{bmatrix}
0 \\
-3 \\
4
\end{bmatrix}= \ \huge?\)

Answer 2

@atercero

Answer 3

this shouldn't be difficult ... they are
[1,0,0], [0,1,0], [0,0,1] spans R^3 ... find
a, b ,c ... such that a[1,0,0]+b[0,1,0]+c [0,0,1] = [0,-3,4]

then use the definition of Linearity.