Compute \(\begin{pmatrix}1&2\\3&4\end{pmatrix}\) + \(\begin{pmatrix}5&-1\\0&7\end{pmatrix}\).

Can a \(2\times 3\) matrix be added to a \(3\times 2\) matrix? Explain.

Compute \(\begin{pmatrix}2&-3&1\end{pmatrix}\) + \(\begin{pmatrix}4&0&-5\end{pmatrix}\).

Find A + 0 for \(A=\begin{pmatrix}-2&5\\1&3\end{pmatrix}\), where 0 is the \(2\times 2\) zero matrix.

Find the additive inverse of \(A=\begin{pmatrix}3&-2\\0&6\end{pmatrix}\).

Find x and y if \(\begin{pmatrix}x&1\\2&y\end{pmatrix}\) + \(\begin{pmatrix}3&4\\-2&5\end{pmatrix}\) = \(\begin{pmatrix}7&5\\0&1\end{pmatrix}\).

Compute A + B + C for \(A=\begin{pmatrix}1&0\\2&1\end{pmatrix}\), \(B=\begin{pmatrix}3&-1\\0&4\end{pmatrix}\), and C = \(\begin{pmatrix}-2&5\\1&-3\end{pmatrix}\).

Show with \(A=\begin{pmatrix}1&2\\0&-1\end{pmatrix}\) and \(B=\begin{pmatrix}3&-5\\4&2\end{pmatrix}\) that \(A+B=B+A\).

Find B if \(A+B=C\), where \(A=\begin{pmatrix}2&1\\-3&4\end{pmatrix}\) and C = \(\begin{pmatrix}0&5\\7&-2\end{pmatrix}\).

A student claims \(\begin{pmatrix}1&2&3\end{pmatrix}\) + \(\begin{pmatrix}4\\5\\6\end{pmatrix}\) = \(\begin{pmatrix}5&7&9\end{pmatrix}\). Diagnose the error.