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Explain solution rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 35

Answers (1)

option (c) \lambda =1

Given -  \begin{bmatrix} 2 & -1 &3 \\ \lambda &0 &7 \\ -1& 1 &4 \end{bmatrix}

Hint – Find the determinant of A i.e, \left | A \right |  

Solution – since matrix is not invertible

 \begin{aligned} &\therefore|\mathrm{A}|=0 \\ &\mathrm{~A}=\left[\begin{array}{ccc} 2 & -1 & 3 \\ \lambda & 0 & 7 \\ -1 & 1 & 4 \end{array}\right] \\ &|\mathrm{A}|=2(0-7)+1(4 \lambda+7)+3(\lambda+0) \\ &0=-14+4 \lambda+7+3 \lambda \quad(\therefore|\mathrm{A}|=0) \\ &0=-7+7 \boldsymbol{\lambda} \\ &7=7 \boldsymbol{\lambda} \\ &\Rightarrow \lambda=1 \end{aligned}

Hence, option (c) is correct

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