Chapter 6, Problem 1RE

To determine

To calculate: The value of $A+B$ for the matrices $A=\left[\begin{array}{cc}2& -3\\ -2& 4\end{array}\right],B=\left[\begin{array}{cc}3& 7\\ 1& 2\end{array}\right]$.

Answer to Problem 1RE

Solution:

The value of $A+B$ is $\left[\begin{array}{cc}5& 4\\ -1& 6\end{array}\right]$.

Explanation of Solution

Given:

The matrices $A=\left[\begin{array}{cc}2& -3\\ -2& 4\end{array}\right],B=\left[\begin{array}{cc}3& 7\\ 1& 2\end{array}\right]$.

Formula Used:

Two matrices can only be subtracted if they have the same size and the difference corresponds to the matrix with entries as the difference of the corresponding entries of the two matrices.

Calculation:

Both the matrices have the same order $2\times 2$. Hence, the sum can be computed as:

$\begin{array}{c}A+B=\left[\begin{array}{cc}2& -3\\ -2& 4\end{array}\right]+\left[\begin{array}{cc}3& 7\\ 1& 2\end{array}\right]\\ =\left[\begin{array}{cc}2+3& -3+7\\ -2+1& 4+2\end{array}\right]\\ =\left[\begin{array}{cc}5& 4\\ -1& 6\end{array}\right]\end{array}$

The desired matrix is $\left[\begin{array}{cc}5& 4\\ -1& 6\end{array}\right]$.