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  • please solve rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice questions question 8 maths textbook solution

please solve rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice questions question 8 maths textbook solution

Answers (1)

:  option (a) 144   

Given: A= \begin{bmatrix} 1& 2 & -1 \\ -1& 1& 2\\ 2& -1& 1 \end{bmatrix}

Hint: calculate adjoint of A and put the value in it.

Solution:
\begin{aligned} &A=\left[\begin{array}{ccc} 1 & 2 & -1 \\ -1 & 1 & 2 \\ 2 & -1 & 1 \end{array}\right] \\ &|A|=1(1+2)-2(-1-4)-1(1-2) \\ &=3+10+1=14 \\ &|A| \neq 0 \\ &\Rightarrow \operatorname{adj}(\operatorname{adj} A)=|A|^{(n-1)^{2}} \mid \end{aligned} 

Where n=3 because of 3×3 matrices 

\begin{aligned} &=|A|^{(3-1)^{2}} \\ &=|A|^{2^{2}} \\ &=|A|^{4} \\ &=14^{4} \quad(\therefore|\mathrm{A}|=14) \\ \end{aligned}

Hence, option (a) is correct.

 

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