If a matrix A is such that \[3A^3 + 2 A^2 + 5 A + I = 0,\text{ then }A^{- 1}\] equal to _______________ .

If a Matrix a is Such that 3 a 3 + 2 a 2 + 5 a + I = 0 , Then a − 1 Equal to - Mathematics

प्रश्न

If a matrix A is such that $3 A^{3} + 2 A^{2} + 5 A + I = 0, then A^{- 1}$ equal to _______________ .

पर्याय

$- (3 A^{2} + 2 A + 5)$
$3 A^{2} + 2 A + 5$
$3 A^{2} - 2 A - 5$
none of these

MCQ

उत्तर

None of these

$3 A^{3} + 2 A^{2} + 5 A + I = 0$

$\Rightarrow 3 A^{3} + 2 A^{2} + 5 A = - I$

$\Rightarrow A^{- 1} (3 A^{3} + 2 A^{2} + 5 A) = - I A^{- 1}$

$\Rightarrow 3 A^{2} + 2 A + 5 I = - A^{- 1}$

$\Rightarrow A^{- 1} = - 3 A^{2} - 2 A - 5 I$

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Inverse of Matrix - Inverse of a Square Matrix by the Adjoint Method

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Q 28 Q 27 Q 29

पाठ 7: Adjoint and Inverse of a Matrix - Exercise 7.4 [पृष्ठ ३९]

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आरडी शर्मा Mathematics [English] Class 12

पाठ 7 Adjoint and Inverse of a Matrix
Exercise 7.4 | Q 28 | पृष्ठ ३९

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If a Matrix a is Such that 3 a 3 + 2 a 2 + 5 a + I = 0 , Then a − 1 Equal to - Mathematics

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