If A = 2 2 9 4 and I = 1 0 0 1 , then 10 A - 1 , is equal to.

Characteristics equation of matrix A is A - x I = 0 . 2 2 9 4 - x 1 0 0 1 = 0 ⇒ 2 - x 9 2 4 - x = 0 ⇒ x 2 - 6 x - 10 = 0 ∴ A 2 - 6 A - 10 I = 0 10 A - 1 = A - 6 I .

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MathematicsMatrixInverse matrixMedium2 minPYQ_2020

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If $A = (\begin{matrix} 2 & 2 \\ 9 & 4 \end{matrix})$ and $I = (\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}),$ then $10 A^{- 1}$ , is equal to.

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Solution:

Characteristics equation of matrix $A$ is $A - x I = 0$ .

$(\begin{matrix} 2 & 2 \\ 9 & 4 \end{matrix}) - x (\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}) = 0$
$\Rightarrow |\begin{matrix} 2 - x \\ 9 \end{matrix} \begin{matrix} 2 \\ 4 - x \end{matrix}| = 0 \Rightarrow x^{2} - 6 x - 10 = 0$

$∴ A^{2} - 6 A - 10 I = 0$
$10 A^{- 1} = A - 6 I$ .

Stream:JEESubject:MathematicsTopic:MatrixSubtopic:Inverse matrix

⏱ 2mℹ️ Source: PYQ_2020

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