Question

Perform the indicated matrix operation.

$\left[\begin{array}{cc}5& -6\\ -9& 4\end{array}\right]\mathbf{+}\left[\begin{array}{cc}2& -3\\ -4& 2\end{array}\right]$

Short answer

The addition of the matrices is $\left[\begin{array}{cc}5& -6\\ -9& 4\end{array}\right]\mathbf{+}\left[\begin{array}{cc}2& -3\\ -4& 2\end{array}\right]\mathbf{=}\left[\begin{array}{cc}7& -9\\ -13& 6\end{array}\right]$.

Step-by-step solution

Step 1. Define the concept of matrix addition.

If $A$and $B$are two matrices of order $m\times n$, then the addition of the two matrices will also yield a matrix of order$m\times n$ wherein each element is the sum of the corresponding elements.

Step 2. Add corresponding elements.

In order to find$\left[\begin{array}{cc}5& -6\\ -9& 4\end{array}\right]+\left[\begin{array}{cc}2& -3\\ -4& 2\end{array}\right]$, add corresponding elements of both the matrices.

$\left[\begin{array}{cc}5& -6\\ -9& 4\end{array}\right]+\left[\begin{array}{cc}2& -3\\ -4& 2\end{array}\right]=\left[\begin{array}{cc}5+2& -6-3\\ -9-4& 4+2\end{array}\right]$

Step 3. Simplify the matrix.

Further simplify the matrix by adding the elements.

$\begin{array}{c}\left[\begin{array}{cc}5& -6\\ -9& 4\end{array}\right]+\left[\begin{array}{cc}2& -3\\ -4& 2\end{array}\right]=\left[\begin{array}{cc}5+2& -6-3\\ -9-4& 4+2\end{array}\right]\\ =\left[\begin{array}{cc}7& -9\\ -13& 6\end{array}\right]\end{array}$