Chapter CSB1.16, Problem 3E

To determine

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

Answer to Problem 3E

The difference of matrices ${\left[\begin{array}{c}11\\ 16\\ 4\end{array}\right]}_{3\times 1}$ and ${\left[\begin{array}{c}7\\ 19\\ 2\end{array}\right]}_{3\times 1}$ is ${\left[\begin{array}{c}4\\ -3\\ 2\end{array}\right]}_{3\times 1}$ .

Explanation of Solution

Given information:

The given difference of matrices is $\left[\begin{array}{c}11\\ 16\\ 4\end{array}\right]-\left[\begin{array}{c}7\\ 19\\ 2\end{array}\right]$ .

Calculations:

The given matrices $A={\left[\begin{array}{c}11\\ 16\\ 4\end{array}\right]}_{3\times 1}$ and $B={\left[\begin{array}{c}7\\ 19\\ 2\end{array}\right]}_{3\times 1}$ are of same order $3\times 1$ , so they can be subtracted.

  $A-B={\left[\begin{array}{c}11\\ 16\\ 4\end{array}\right]}_{3\times 1}-{\left[\begin{array}{c}7\\ 19\\ 2\end{array}\right]}_{3\times 1}$

  $\Rightarrow A-B={\left[\begin{array}{c}11-7\\ 16-19\\ 4-2\end{array}\right]}_{3\times 1}$

  $\Rightarrow A-B={\left[\begin{array}{c}4\\ -3\\ 2\end{array}\right]}_{3\times 1}$

Thus, the difference of matrices ${\left[\begin{array}{c}11\\ 16\\ 4\end{array}\right]}_{3\times 1}$ and ${\left[\begin{array}{c}7\\ 19\\ 2\end{array}\right]}_{3\times 1}$ is ${\left[\begin{array}{c}4\\ -3\\ 2\end{array}\right]}_{3\times 1}$ .

Conclusion:

The difference of matrices ${\left[\begin{array}{c}11\\ 16\\ 4\end{array}\right]}_{3\times 1}$ and ${\left[\begin{array}{c}7\\ 19\\ 2\end{array}\right]}_{3\times 1}$ is ${\left[\begin{array}{c}4\\ -3\\ 2\end{array}\right]}_{3\times 1}$ .