This is a part of a larger problem that I know the answer to but I was wondering if someone could explain or maybe give me a visual representation of how adding matrices works.
So I know that $e_1 = \begin{bmatrix}1 \\ 0 \\ \end{bmatrix}$
I also know that $e_2 = \begin{bmatrix}0 \\ 1 \\ \end{bmatrix}$
This is because the origin should be $\begin{bmatrix}1 & 0\\ 0 & 1\\ \end{bmatrix}$
So then my directions say that I'm trying to find the horizontal shear transformation by letting $e_1$ stay the same but I need to let $e_2$ change to $e_2 + 3*e_1$
My conclusion for $e_2$
$e_2 = \begin{bmatrix}0 \\ 1 \\ \end{bmatrix} + 3 * \begin{bmatrix}1 \\ 0 \\ \end{bmatrix} $
$e_2 = \begin{bmatrix}0 \\ 1 \\ \end{bmatrix} + \begin{bmatrix} 3 \\ 0 \\ \end{bmatrix} $
New $e_2 = \begin{bmatrix}3 \\ 1 \\ \end{bmatrix} $
This is the answer because I'm taking 0 + 3 from row 1 and 1 + 0 from row 2 right?