Suggested languages for you:

Americas

Europe

Q24.

Expert-verified
Found in: Page 164

### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

# Use matrices $A$, $B$, $C$ and $D$ to find the following.$A=\left[\begin{array}{cc}5& 7\\ -1& 6\\ 3& -9\end{array}\right],\text{\hspace{0.17em}\hspace{0.17em}}B=\left[\begin{array}{cc}8& 3\\ 5& 1\\ 4& 4\end{array}\right],\text{\hspace{0.17em}\hspace{0.17em}}C=\left[\begin{array}{cc}0& 4\\ -2& 5\\ 7& -1\end{array}\right],\text{\hspace{0.17em}\hspace{0.17em}}D=\left[\begin{array}{cc}6& 2\\ 9& 0\\ -3& 0\end{array}\right]$24. $A+B$

The final matrix after performing the indicated matrix operations is $A+B=\left[\begin{array}{cc}13& 10\\ 4& 7\\ 7& -5\end{array}\right]$.

See the step by step solution

## Step 1 - Substitute the matrices

Substitute $\left[\begin{array}{cc}5& 7\\ -1& 6\\ 3& -9\end{array}\right]$ for A and $\left[\begin{array}{cc}8& 3\\ 5& 1\\ 4& 4\end{array}\right]$ for B into .

$A+B=\left[\begin{array}{cc}5& 7\\ -1& 6\\ 3& -9\end{array}\right]+\left[\begin{array}{cc}8& 3\\ 5& 1\\ 4& 4\end{array}\right]$

## Step 2 - Perform the matrix addition

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

$\begin{array}{c}A+B=\left[\begin{array}{cc}5& 7\\ -1& 6\\ 3& -9\end{array}\right]+\left[\begin{array}{cc}8& 3\\ 5& 1\\ 4& 4\end{array}\right]\\ =\left[\begin{array}{cc}5+8& 7+3\\ -1+5& 6+1\\ 3+4& -9+4\end{array}\right]\end{array}$

## Step 3 - Simplify

Further simplify the matrix.

$\begin{array}{c}A+B=\left[\begin{array}{cc}5+8& 7+3\\ -1+5& 6+1\\ 3+4& -9+4\end{array}\right]\\ =\left[\begin{array}{cc}13& 10\\ 4& 7\\ 7& -5\end{array}\right]\end{array}$