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Determinants — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDeterminants1 Mark
Question
For the matrix $A=\left[\begin{array}{ccc}2 & -1 & 1 \\ \lambda & 2 & 0 \\ 1 & -2 & 3\end{array}\right]$ to be invertible, the value of $\lambda$ is
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Answer

Given, $A=\left[\begin{array}{ccc}2 & -1 & 1 \\ \lambda & 2 & 0 \\ 1 & -2 & 3\end{array}\right]$
For invertible matrix, $|A| \neq 0$
So, $2(6-0)+1(3 \lambda-0)+1(-2 \lambda-2) \neq 0$
$\Rightarrow \quad 12+3 \lambda-2 \lambda-2 \neq 0$
$\Rightarrow \lambda+10 \neq 0 \Rightarrow \lambda \neq-10$
$\therefore \quad$ Required value of $\lambda$ is $R-\{-10\}$.

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