Question

Find the sum of the matrices. \(\left[\begin{array}{ll}5 & -2 \\ 5 & -1\end{array}\right]+\left[\begin{array}{rr}-1 & -16 \\ 11 & -3\end{array}\right]\)

Short answer

The sum of the matrices is \[\left[\begin{array}{ll}4 & -18 \ 16 & -4\end{array}\right]\]

Step-by-step solution

Identify corresponding elements

Corresponding elements are located at the same position in both matrices. For example, the top left element in both matrices are 5 and -1.

Add corresponding elements

Add each pair of corresponding elements together. This gives us \(5 + -1 = 4\) for the top left position, \(-2 + -16 = -18\) for the top right position, \(5 + 11 = 16\) for the bottom left position, and \(-1 + -3 = -4\) for the bottom right position.

Write the Resulting Matrix

Place these sums in their corresponding positions in the resulting matrix. The resulting matrix is \[\left[\begin{array}{ll}4 & -18 \ 16 & -4\end{array}\right]\]