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  • Need solution for RD Sharma Maths Class 12 Chapter 6 Adjoint and Inverse of Matrix Excercise Fill in the blanks Question 4

Need solution for RD Sharma Maths Class 12 Chapter 6 Adjoint and Inverse of Matrix Excercise Fill in the blanks  Question 4

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Answer 

Hint   \rightarrow A matrix is non-invertible if and only if  \left | A \right |=0

Given              \rightarrow A=\begin{bmatrix} 1 & a & 2\\ 1 & 2 & 5\\ 2 & 1 & 1 \end{bmatrix}   is not invertible

Explanation       \rightarrow \left | A \right |=\begin{bmatrix} 1 & a & 2\\ 1 & 2 & 5\\ 2 & 1 & 1 \end{bmatrix}=0

Expanding along first row

                \begin{aligned} &1(2-5)-a(1-10)+2(1-4)=0 \\\\ &-3+9 a-6=0 \\\\ &9 a=9 \\\\ &a=1 \end{aligned}

Hence,      a=1

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