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Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1)...

Let `A=((1,0,0),(2,1,0),(3,2,1))`. If `u_(1)` and `u_(2)` are column matrices such that `Au_(1)=((1),(0),(0))` and `Au_(2)=((0),(1),(0))`, then `u_(1)+u_(2)` is equal to :

A

`((-1),(1),(0))`

B

`((-1),(1),(-1))`

C

`((-1),(-1),(0))`

D

`((1),(-1),(-1))`

Text Solution

Verified by Experts

The correct Answer is:
D
`A(u_(1)+u_(2))=[(1),(1),(0)]`
Now `|A|=1`
`A^(-1)=1/(|A|)` adj A
`u_(1)+u_(2)=A^(-1) [(1),(1),(0)]=[(1,0,0),(-2,1,0),(1,-2,1)][(1),(1),(0)]=[(1),(-1),(-1)]`
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