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Statement-1 (Assertion and Statement- 2 ...

Statement-1 (Assertion and Statement- 2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. Statement -1 If `A= [[1,-1,-1],[1,-1,0],[1,0,-1]]` then `A^(3) + A^(2) + A= I ` Statement - 2 If `det (A-lambdaI) = C_(0) lambda^(3) + C_(1) lambda^(2) + C_(2)lambda + C_(3) = 0.` then ` C_(0) A^(3) + C_(1)A ^(2) + C_(2)A + C_(3)I = O.`

A

Statement-1 is true, Statement -2 is true, Statement-2
is a correct explanation for Statement-1

B

Statement-1 is true, Statement-2 is true, Sttatement - 2
is not a correct explanation for Stamtement-1

C

Statement 1 is true, Statement - 2 is false

D

Statement-1 is false, Statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
D
`therefore det (A - lambdaI) = [[1-lambda,-1,-1],[1,-1-lambda,0],[1,0,-1-lambda]]=0`
`rArr (1-lambda ) (1+lambda)^(2) - 1-lambda -1 -lambda = 0`
`rArr lambda^(3) + lambda^(2) + lambda + 1= 0`
` rArr A^(3) + A^(2) + A + I = 0`
`rArr A^(3) + A^(2) + A= -I`
Statement -1 is false but Statement -2 is true.
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