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  • Explain solution RD Sharma class 12 Chapter 6 Adjoint and Inverse of a Matrix exercise Fill in the blanks question 24

Explain solution RD Sharma class 12 Chapter 6 Adjoint and Inverse of a Matrix exercise Fill in the blanks question 24

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Answer   \rightarrow 79

Hint   \rightarrow \text { Aadj } A=|A| I

Given    \rightarrow A=\left[\begin{array}{lll} x & 5 & 2 \\ 2 & y & 3 \\ 1 & 1 & z \end{array}\right] x y z=80,3 x+2 y+10 z=20

Explanation    \rightarrow|A|=\left|\begin{array}{lll} x & 5 & 2 \\ 2 & y & 3 \\ 1 & 1 & z \end{array}\right|

                \begin{aligned} &=x(y z-3)-5(2 z-3)+2(2-y) \\ &=x y z-3 x-10 z+15+4-2 y \\ &=x y z-(3 x+2 y+10 z)+19 \\ &=80-20+19 \\ &=79 \end{aligned}

               

               

               

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