Q.Find $x$ and $y$, if $\begin{bmatrix} 2x+y & -1 & 1 \\ 3 & 4y & 4 \end{bmatrix} + \begin{bmatrix} -1 & 6 & 4 \\ 3 & 0 & 3 \end{bmatrix} = \begin{bmatrix} 3 & 5 & 5 \\ 6 & 18 & 7 \end{bmatrix}$

Given $\begin{bmatrix} 2x+y & -1 & 1 \\ 3 & 4y & 4 \end{bmatrix} + \begin{bmatrix} -1 & 6 & 4 \\ 3 & 0 & 3 \end{bmatrix} = \begin{bmatrix} 3 & 5 & 5 \\ 6 & 18 & 7 \end{bmatrix}$.

Add the left-hand matrices entry-wise:

$\begin{bmatrix} (2x+y)+(-1) & -1+6 & 1+4 \\ 3+3 & 4y+0 & 4+3 \end{bmatrix} = \begin{bmatrix} 2x+y-1 & 5 & 5 \\ 6 & 4y & 7 \end{bmatrix}$

By equality of matrices, comparing entries with the right-hand side $\begin{bmatrix} 3 & 5 & 5 \\ 6 & 18 & 7 \end{bmatrix}$ (the entries 5,5,6,7 already match, confirming the arithmetic): …

Add the two given matrices entry-wise on the left, then equate corresponding entries with the right-ha …

• Forgetting to add the constant −1 into the (1,1) entry before equating with 3, i.e. solving $2x+y=3$ instead of $2x+y-1=3$. …