I am trying to solve this question;
The $2\times 2$ elementary matrix $E$ can be gotten from the identity matrix using the row operation R1 = r1 + 2 r2. Find $EA$ if $$A=\begin{bmatrix} 50\\ 51 \end{bmatrix}$$
($A$ is a $2\times1$ matrix)
I found the answer which is a $2\times 1$ matrix
$$\begin{bmatrix}152\\ 51 \end{bmatrix}$$
But the answer for this question is a $2\times 2$ matrix. (The book says so)
Is the question wrong or I'm doing a mistake?
Thanks.
You may find the question below.
This is some pretty terrible typesetting in the picture. I would totally interpret this as a $2\times 1$ matrix as well, the way it appears.
However, it is entirely possible this is just a display problem, and the matrix was actually meant to be $2\times 2$.
Amusingly, the answers either way are similar: $$\begin{bmatrix}1&2\\ 0&1\end{bmatrix}\begin{bmatrix}5&0\\ 5&1\end{bmatrix}=\begin{bmatrix}15&2\\ 5&1\end{bmatrix}$$
and
$$\begin{bmatrix}1&2\\ 0&1\end{bmatrix}\begin{bmatrix}50 \\ 51\end{bmatrix}=\begin{bmatrix}152\\ 51\end{bmatrix}$$
It looks like you are analyzing the dimensions of the products of matrices correctly, so good job. I think the answer to this question entirely hinges upon asking the author what this is supposed to read. I'm betting it's just failed typesetting.