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|(a, a^2, 0), (1, 2a+b ,(a+b)), (0, 1, ...

`|(a, a^2, 0), (1, 2a+b ,(a+b)), (0, 1, 2a+3b)|` is divisible by
a. `a+b`
b. `a+2b`
c. `2a+3b`
d. `a^2`

A

`a+b `

B

`a+2b`

C

`2a+3b`

D

`a^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`Delta = |{:(a,,a^(2),,0),(1,,2a+b,,(a+b)),(0,,1,,2a+2b):}|`
`=a |{:(1,,a,,0),(1,,(2a+b),,(a+b)),(0,,1,,2a+3b):}|`
`=a(a+b) |{:(1,,a,,0),(0,,1,,(a+b)),(0,,1,,2a+3b):}|" "(R_(2) to R_(2) -R_(1))`
`=a(a+b) (2a+3b-a-b)`
`=a(a+b) (a+2b)`
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