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] =

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] =

zzr0ck3r · Answer

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

zzr0ck3r · Answer

@atercero

experimentx · Answer

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.