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Let A=[[1 ,2 ,3],[ 2, 0, 5],[ 0 ,2 ,1]] ...

Let `A=[[1 ,2 ,3],[ 2, 0, 5],[ 0 ,2 ,1]] and B=[[0],[-3],[1]]` . Which of the following is a true? a.`A X=B` has a unique solution b.`A X=B` has exactly three solutions c.`A x=B` has infinitely many solutions d.`A X=B` is inconsistent

A

`AX=B` has a unique solution

B

`AX=B` has exactly three solutions

C

`AX=B` has infinitelt many solutions

D

`AX=B` is inconsistent

Text Solution

Verified by Experts

The correct Answer is:
A
`|A|=1 (0-10)-2(2-0)+3(4-0)`
`=-10-4+12=-2`
`implies |A| ne 0`
`implies` Unique solution
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