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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?

The Count
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Liath
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  • Yes. Your conclusion is correct, though you have a typo in the derivation ($[1, 3]^T$ should be $[1, 0]^T$). In general, the sum of two matrices is defined when the operands have the same number of rows and the same number of columns. Each element of the sum is the sum of the corresponding elements. – Fabio Somenzi Feb 01 '18 at 05:24
  • I fixed that error. Didn't realize I did it. Thanks! – Liath Feb 01 '18 at 05:41

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