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The value of |{:(sqrt(13 )+ sqrt(3), 2sq...

The value of `|{:(sqrt(13 )+ sqrt(3), 2sqrt(5),sqrt(5)),(sqrt(15) + sqrt(26),5,sqrt(10)),(3 + sqrt(65), sqrt(15),5):}|`

A

`sqrt(3) (5 - sqrt(6))`

B

`-5 sqrt(3) (5 - sqrt(6))`

C

`5 sqrt(3) (5 - sqrt(6))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`=|{:(sqrt(13),2sqrt(5),sqrt(5)),(sqrt(15),5,sqrt(10)),(3,sqrt(15),5):}| + |{:(sqrt(3),2sqrt(5),sqrt(5)),(sqrt(26),5,sqrt(10)),(sqrt(65),sqrt(15),5):}|`
`= (sqrt(2))^(2) |{:(sqrt(13),2,1),(sqrt(15),sqrt(5),sqrt(2)),(3,sqrt(3),sqrt(5)):}| + (sqrt(5))^(2) |{:(sqrt(3),2,1),(sqrt(26),sqrt(5),sqrt(2)),(sqrt(65),sqrt(3),sqrt(5)):}|`
`C_(1) to C_(1) = sqrt(3) C_(2)` `C_(1) to C_(1) - sqrt(13) C_(3)`
`= 5 |{:(sqrt(13)-2 sqrt(3),2,1),(0,sqrt(5),sqrt(2)),(0,sqrt(3),sqrt(5)):}| + 5 |{:(sqrt(3) - sqrt(13),2,1),(0,sqrt(5),sqrt(2)),(0,sqrt(3),sqrt(5)):}|`
`=5 [(sqrt(13) - 3 2 sqrt(3)) (5 - sqrt(6))+ (sqrt(3) - sqrt(13)) (5 - sqrt(6))]`
`= 5 [5 - sqrt(6)][- sqrt(3)]`
`=- 5 sqrt(3) (5 - sqrt(6))`
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