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

If `A =((1,0,0),(2,1,0),(3,2,1)) u_(1) and u_(2)` are the 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:
B
Let `u_(1) + u_(2) = ((x),(y),(z))`
Now, `Au_(1) + Au_(2) = ((1),(1),(0))`
`rArrA(u_(1) + u_(2)) = ((1),(1),(0))`
`rArr ((1,0,0),(2,1,0),(3,2,1)) ((x),(y),(z)) = ((1),(1),(0))`
`rArr ((x),(2x+y),(3x+2y+z)) = ((1),(1),(0))`
`therefore x = 1, 2x + y =1`
and ` 3x + 2y +=0`
`rArr x=1, y=-1, z=-1` Hence, `u_(1) + u_(2) = ((1),(-1),(1))`
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