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Mathematics - Matrices Question with Solution | TestHub

MathematicsMatricesAdjointMedium2 minPYQ_2020

MathematicsMediumsingle choice

Let A be a $3 \times 3$ matrix such that $adj A = [\begin{matrix} 2 & - 1 & 1 \\ - 1 & 0 & 2 \\ 1 & - 2 & - 1 \end{matrix}]$ and $B = adj (a d j A)$ . If $| A | = λ$ and $|{(B^{- 1})}^{⊤}| = μ$ , then the ordered pair $(|λ|, μ)$ is equal to

Options:

Answer:

A

Solution:

$|a d j A| = {|A|}^{2} = 9$

$\Rightarrow |A| = \pm 3 = λ \Rightarrow |λ| = 3$

$\Rightarrow |B| = {|a d j A|}^{2} = 81$

$\Rightarrow |{(B^{- 1})}^{T}| = |B^{- 1}| = {|B|}^{- 1} = \frac{1}{|B|} = \frac{1}{81} = μ$

$∴ (|λ|, μ) = (3, \frac{1}{81})$ .

Stream:JEESubject:MathematicsTopic:MatricesSubtopic:Adjoint

⏱ 2mℹ️ Source: PYQ_2020

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