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

Question No.1

1. Order of A is 2 by 2
2. Order of B is 2 by 3
3. Order of C is 3 by 1
4. Order of D is 1 by 3

Question No.2

A = D, B = E, C = F

Question No.3

• A = Square Matrix
• B = Identity Matrix
• C = Row Matrix
• D = Zero or Null Matrix
• E = Rectangular Matrix
• F = Column Matrix

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