Chapter 4, Problem 8MCQ

To determine

Tofind:the matrix using indicated operation if it exists.

Answer to Problem 8MCQ

The matrix after operation is $\left[\begin{array}{c}\text{4-15x}\\ \text{9}\\ \text{4x-15}\end{array}\right]$ .

Explanation of Solution

Given:

  $\text{2}\left[\begin{array}{c}\text{-1}\\ \text{5}\\ \text{-6}\end{array}\right]\text{+4}\left[\begin{array}{c}\text{-3x}\\ \text{2}\\ \text{x}\end{array}\right]\text{-3}\left[\begin{array}{c}\text{x-2}\\ \text{3}\\ \text{1}\end{array}\right]$ .

Concept used:

Addition of matrix can be calculated as:

  $\left[\begin{array}{cc}{\text{a}}_{\text{11}}& {\text{a}}_{\text{12}}\\ {\text{a}}_{\text{13}}& {\text{a}}_{\text{14}}\end{array}\right]\text{+}\left[\begin{array}{cc}{\text{b}}_{\text{11}}& {\text{b}}_{\text{12}}\\ {\text{b}}_{\text{13}}& {\text{b}}_{\text{4}}\end{array}\right]\text{=}\left[\begin{array}{cc}{\text{a}}_{\text{11}}{\text{+b}}_{\text{11}}& {\text{a}}_{\text{12}}{\text{+b}}_{\text{12}}\\ {\text{a}}_{\text{13}}{\text{+a}}_{\text{13}}& {\text{a}}_{\text{14}}{\text{+b}}_{\text{14}}\end{array}\right]$ .

Calculation:

  $\text{2}\left[\begin{array}{c}\text{-1}\\ \text{5}\\ \text{-6}\end{array}\right]\text{+4}\left[\begin{array}{c}\text{-3x}\\ \text{2}\\ \text{x}\end{array}\right]\text{-3}\left[\begin{array}{c}\text{x-2}\\ \text{3}\\ \text{1}\end{array}\right]$ .

  $\left[\begin{array}{c}\text{2}\times \text{-1}\\ \text{2}\times \text{5}\\ \text{2}\times \text{-6}\end{array}\right]\text{+}\left[\begin{array}{c}\text{4}\times \text{-3x}\\ \text{4}\times \text{2}\\ \text{4}\times \text{x}\end{array}\right]-\left[\begin{array}{c}\text{3}\left(\text{x-2}\right)\\ \text{3}\times \text{3}\\ \text{3}\times \text{1}\end{array}\right]$ .

  $\Rightarrow \left[\begin{array}{c}\text{-2-12x-3x-}\left(\text{-6}\right)\\ \text{10+8-9}\\ \text{-12+4x-3}\end{array}\right]\text{=}\left[\begin{array}{c}\text{4-15x}\\ \text{9}\\ \text{4x-15}\end{array}\right]$ .

Hence, the matrix after operation is $\left[\begin{array}{c}\text{4-15x}\\ \text{9}\\ \text{4x-15}\end{array}\right]$ .