Question 11, Exercise 2.2

Solutions of Question 11 of Exercise 2.2 of Unit 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.

Identify singular and non-singular matrices. $\left[ \begin{matrix}7 & 1 & 3 \\6 & 2 & -2 \\5 & 1 & 1\end{matrix} \right]$

Let $$A=\left[ \begin{matrix} 7 & 1 & 3 \\ 6 & 2 & -2 \\ 5 & 1 & 1 \\ \end{matrix} \right]$$ $$|A|=7(2+2)-1(6+10)+3(6-10)$$ $$=28-16-12$$ $$|A|=0$$ $A$ is singular.

Identify singular and non-singular matrices. $\left[ \begin{matrix}1 & -1 & 1 \\3 & -2 & 1 \\-2 & -3 & 2 \end{matrix} \right]$

Let $$A=\left[ \begin{matrix} 1 & -1 & 1 \\ 3 & -2 & 1 \\ -2 & -3 & 2 \\ \end{matrix} \right]$$ $$|A|=1(-4+3)+1(6+2)+1(-9-4)$$ $$=-1+8-13$$ $$|A|=-6$$ $A$ is not equal to zero. Then $A$ is non-singular.

Identify singular and non-singular matrices. $\left[ \begin{matrix}3 & 2 & -3 \\3 & 6 & -3 \\-1 & 0 & 1 \end{matrix} \right]$

Let $$A=\left[ \begin{matrix} 3 & 2 & -3 \\ 3 & 6 & -3 \\ -1 & 0 & 1 \\ \end{matrix} \right]$$ $$|A|=3(6)-2(3-3)-3(6)$$ $$|A|=0$$ $A$ is singular.