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Let A=[{:(-5,-8,-7),(3,5,4),(2,3,3):}] a...

Let `A=[{:(-5,-8,-7),(3,5,4),(2,3,3):}]` and `B=[{:(x),(y),(1):}]`. If `AB` is a scalar multiple of `B`, then the value of `x+y` is

A

`-1`

B

`-2`

C

`1`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `AB=lambdaB`, where `lambda` is non-zero scalar.
`[{:(-5x-8y-7),(3x+5y+4),(2x+3y+3):}]=lambda[{:(x),(y),(2):}]`
i.e., `{:(-5x-8y-7=lambdax),(3x+5y+4=lambday),(2x+3y+3=2lambda):}`
Adding `0=lambda(x+y+2)`
`lambda ne 0impliesx+y+2=0`
`x+y=-2`
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