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Let AX = B be a system of n smultaneous ...

Let AX = B be a system of n smultaneous linear equations with n unknowns.
Statement -1 : If `absA=0and (adjA)B ne 0`, the system is consistent with infinitely many solutions.
Statement -2 : A `(adjA)=absAI`

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, Statement -2 is not a correct explanation for Statement -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
We have , AX = B, where `absA=0`
`rArr (adjA)(AX)=(adjA)B`
`rArr ((adjA)A)X=(adjA)B`
`rArr (absAI)X=(adjA)B [f:' A(adjA)=absAI]`
`rArr absAX-(adjA)B`
Clearly, it is not true when `absA=0 and (adjA)B ne 0`,. So, the system is inconsistent.
Hence, stetement -2 is true and statement -1 is false.
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