Let $A = \begin{bmatrix}
-1 & -4 & -8 \\
8 & -7 & 4 \\
\end{bmatrix}_.$
Define the linear transformation $T: \mathbb{R}^3 \to \mathbb{R}^2$ by $T(x) = Ax$.
Let $u = \begin{bmatrix}
-2\\
1\\
2\\
\end{bmatrix}$ and $v = \begin{bmatrix}
a\\
b\\
c\\
\end{bmatrix}_.$
Find the images of $u$ and $v$ under $T$.
I'm not sure exactly how to do this. What do they mean by find the images? Can someone help me out?
Best Answer
The term "the image of $u$ under $T$" refers to $T(u) = Au$. All that you have to do is multiply the matrix by the vectors.