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Explain solution rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 33

Answers (1)

option (d) none of these

Given -A=\begin{bmatrix} 2 & \lambda &-3 \\ 0&2 &5 \\ 1&1 &3 \end{bmatrix}

Hint- find the value of |A|

Solution –

\begin{aligned} &A=\left[\begin{array}{ccc} 2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3 \end{array}\right] \\ &|A|=2(6-5)-\lambda(0-5)-3(0-2) \\ &|A|=2+5 \lambda+6 \\ &A^{-1} \text { exist if }|A| \neq 0 \\ &\Rightarrow 8+5 \lambda \neq 0 \\ &\Rightarrow \lambda \neq \frac{-8}{5} \end{aligned}

Hence, option (d) is correct

 

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