Matrices Exercises and Solutions

Matrices Exercises and Solutions – Solve these six questions of matrices. The solutions are given at the end.

Question No.1 – Find the order of the following matrices.

$\displaystyle A=\left[ {\begin{array}{*{20}{c}} 3 & 2 \\ 1 & 4 \end{array}} \right]$

$\displaystyle B=\left[ {\begin{array}{*{20}{c}} 1 & 2 & 3 \\ 3 & 2 & 5 \end{array}} \right]$

$\displaystyle C=\left[ {\begin{array}{*{20}{c}} 3 \\ 2 \\ 1 \end{array}} \right]$

$\displaystyle D=\left[ {\begin{array}{*{20}{c}} 2 & 4 & 5 \end{array}} \right]$

Question No.2 – Which of the following matrices are equal?

$\displaystyle A=\left[ {\begin{array}{*{20}{c}} 3 & 2 \\ 1 & 4 \end{array}} \right]$

$\displaystyle B=\left[ {\begin{array}{*{20}{c}} 1 & 3 & 4 \\ 2 & 5 & 6 \\ 3 & 2 & 1 \end{array}} \right]$

$\displaystyle C=\left[ {\begin{array}{*{20}{c}} 3 & 2 \\ 2 & 1 \\ 3 & 4 \end{array}} \right]$

$\displaystyle D=\left[ {\begin{array}{*{20}{c}} 4 & 1 \\ 0 & 1 \end{array}} \right]$

$\displaystyle E=\left[ {\begin{array}{*{20}{c}} 2 & 0 & 2 \\ 1 & 1 & 1 \\ 3 & 2 & 0 \end{array}} \right]$

$\displaystyle F=\left[ {\begin{array}{*{20}{c}} 1 & 2 \\ 2 & 3 \\ 1 & 2 \end{array}} \right]$

Question No.3 – From the following matrices, identify the square, rectangular, row, column, identity, null or zero matrices.

$\displaystyle A=\left[ {\begin{array}{*{20}{c}} 2 & 3 \\ 4 & 5 \end{array}} \right]$

$\displaystyle B=\left[ {\begin{array}{*{20}{c}} 1 & 0 \\ 0 & 1 \end{array}} \right]$

$\displaystyle C=\left[ {\begin{array}{*{20}{c}} 3 & 2 & 1 \end{array}} \right]$

$\displaystyle D=\left[ {\begin{array}{*{20}{c}} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}} \right]$

$\displaystyle E=\left[ {\begin{array}{*{20}{c}} 3 & 2 \\ 1 & 2 \\ 1 & 1 \end{array}} \right]$

$\displaystyle F=\left[ {\begin{array}{*{20}{c}} 3 \\ 2 \\ 5 \end{array}} \right]$

Question No.4 – Find the negative of the following matrices.

$\displaystyle A=\left[ {\begin{array}{*{20}{c}} 2 & 3 \\ 3 & {-4} \end{array}} \right]$

$\displaystyle B=\left[ {\begin{array}{*{20}{c}} 1 & 3 & {-2} \\ 2 & 4 & {-1} \end{array}} \right]$

Question No.5 – Find the transpose of the following matrices.

$\displaystyle A=\left[ {\begin{array}{*{20}{c}} 3 & 1 \\ 2 & 2 \end{array}} \right]$

$\displaystyle B=\left[ {\begin{array}{*{20}{c}} 2 & 2 & 2 \\ 1 & 3 & 1 \end{array}} \right]$

$\displaystyle C=\left[ {\begin{array}{*{20}{c}} 2 & 3 & 2 \end{array}} \right]$

$\displaystyle D=\left[ {\begin{array}{*{20}{c}} 2 & 3 \\ 1 & 2 \\ 3 & 1 \end{array}} \right]$

Question No.6 – Find A+B and A-B

$\displaystyle if\,\,A=\left[ {\begin{array}{*{20}{c}} 2 & 2 \\ 3 & 1 \end{array}} \right]$

$\displaystyle B=\left[ {\begin{array}{*{20}{c}} 3 & 2 \\ 2 & 5 \end{array}} \right]$

Answers

Question No.1

Question No.2

A = D, B = E, C = F

Question No.3

Question No.4

$\displaystyle -A=\left[ {\begin{array}{*{20}{c}} {-2} & {-3} \\ {-3} & 4 \end{array}} \right]$

$\displaystyle -B=\left[ {\begin{array}{*{20}{c}} {-1} & {-3} & 2 \\ {-2} & {-4} & 1 \end{array}} \right]$

Question No.5

$\displaystyle {{A}^{t}}=\left[ {\begin{array}{*{20}{c}} 3 & 2 \\ 1 & 2 \end{array}} \right]$

$\displaystyle {{B}^{t}}=\left[ {\begin{array}{*{20}{c}} 2 & 1 \\ 2 & 3 \\ 2 & 1 \end{array}} \right]$

$\displaystyle {{C}^{t}}=\left[ {\begin{array}{*{20}{c}} 2 \\ 3 \\ 2 \end{array}} \right]$

$\displaystyle {{D}^{t}}=\left[ {\begin{array}{*{20}{c}} 2 & 1 & 3 \\ 3 & 2 & 1 \end{array}} \right]$

Question No.6