If a matrix A is such that 3 A3-2 -160-A2-5 -160-A-I-0- -160-then -160-A-1 equal to-a- -3 -160-A2-2 -160-A-5-b- 3 -160-A2-2 -160-A-5-c- 3 -160-A2-2 -160-A-5-d- none of these

(d) none of these3A3+2A2+5A+I=0 #8658;3A3+2A2+5A= I #8658;A 1(3A3+2A2+5A)= IA 1 #8658;3A2+2A+5I= A 1 #8658;A 1= 3A2 2A 5I ...

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Standard XII

Mathematics

Multiplication of Matrices

If a matrix A...

Question

If a matrix A is such that 3 $A^{3} + 2 A^{2} + 5 A + I = 0, then A^{- 1}$ equal to
(a) $- (3 A^{2} + 2 A + 5)$
(b) $3 A^{2} + 2 A + 5$
(c) $3 A^{2} - 2 A - 5$
(d) none of these

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Solution

(d) 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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If a matrix A is such that 3 A3+2 A2+5 A+I=0, then A-1 equal to (a) -3 A2+2 A+5 (b) 3 A2+2 A+5 (c) 3 A2-2 A-5 (d) none of these

(d) none of these3A3+2A2+5A+I=0⇒3A3+2A2+5A=-I⇒A-1(3A3+2A2+5A)=-IA-1⇒3A2+2A+5I=-A-1⇒A-1=-3A2-2A-5I

If a matrix A is such that 3 $A^{3} + 2 A^{2} + 5 A + I = 0, then A^{- 1}$ equal to
(a) $- (3 A^{2} + 2 A + 5)$
(b) $3 A^{2} + 2 A + 5$
(c) $3 A^{2} - 2 A - 5$
(d) none of these

(d) none of these

$3 A^{3} + 2 A^{2} + 5 A + I = 0 \Rightarrow 3 A^{3} + 2 A^{2} + 5 A = - I \Rightarrow A^{- 1} (3 A^{3} + 2 A^{2} + 5 A) = - I A^{- 1} \Rightarrow 3 A^{2} + 2 A + 5 I = - A^{- 1} \Rightarrow A^{- 1} = - 3 A^{2} - 2 A - 5 I$