Chapter CSB1.16, Problem 2E

To determine

Tofind:The sum or difference of given matrices. If there is no sum or difference, write impossible.

Answer to Problem 2E

The sum of matrices ${\left[\begin{array}{cc}3& 2\\ -2& 8\end{array}\right]}_{2\times 2}$ and ${\left[\begin{array}{cc}5& -2\\ 5& 1\end{array}\right]}_{2\times 2}$ is ${\left[\begin{array}{cc}8& 0\\ 3& 9\end{array}\right]}_{2\times 2}$ .

Explanation of Solution

Given information:

The given sum of matrices is $\left[\begin{array}{cc}3& 2\\ -2& 8\end{array}\right]+\left[\begin{array}{cc}5& -2\\ 5& 1\end{array}\right]$ .

Calculations:

The given matrices $A={\left[\begin{array}{cc}3& 2\\ -2& 8\end{array}\right]}_{2\times 2}$ and $B={\left[\begin{array}{cc}5& -2\\ 5& 1\end{array}\right]}_{2\times 2}$ are of same order $2\times 2$ , so they can be added.

  $A+B={\left[\begin{array}{cc}3& 2\\ -2& 8\end{array}\right]}_{2\times 2}+{\left[\begin{array}{cc}5& -2\\ 5& 1\end{array}\right]}_{2\times 2}$

  $A+B={\left[\begin{array}{cc}3+5& 2+(-2)\\ -2+5& 8+1\end{array}\right]}_{2\times 2}$

  $A+B={\left[\begin{array}{cc}8& 0\\ 3& 9\end{array}\right]}_{2\times 2}$

Thus, the sum of matrices ${\left[\begin{array}{cc}3& 2\\ -2& 8\end{array}\right]}_{2\times 2}$ and ${\left[\begin{array}{cc}5& -2\\ 5& 1\end{array}\right]}_{2\times 2}$ is ${\left[\begin{array}{cc}8& 0\\ 3& 9\end{array}\right]}_{2\times 2}$

Conclusion:

The sum of matrices ${\left[\begin{array}{cc}3& 2\\ -2& 8\end{array}\right]}_{2\times 2}$ and ${\left[\begin{array}{cc}5& -2\\ 5& 1\end{array}\right]}_{2\times 2}$ is ${\left[\begin{array}{cc}8& 0\\ 3& 9\end{array}\right]}_{2\times 2}$ .