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Which of the following determinants have...

Which of the following determinants have value 'zero'?
1. `|{:(41,1,5),(79,7,9),(29,5,3):}|`
2. `|{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|`
3. `|{:(0,c,b),(-c,0,a),(-b,-a,0):}|`
Select the correct answer using the code given below.

A

1 and 2 only

B

2 and 3 only

C

1 and 3 only

D

1, 2 and 3

Text Solution

Verified by Experts

The correct Answer is:
D
1. `|(41,1,5),(79,7,9),(29,5,3)|=|(40,1,5),(72,7,9),(24,5,3)|" "C_(1)rarrC_(1)-C_(2)`
`=|(5,1,5),(9,7,9),(3,5,3)|=0`
`because " to columns are same so value of determinnant is zero"`
2. `|(1,a,b+c),(1,a+b+c,c+a),(1,a+b+c,a+b)|C_(2)rarrC_(2)+C_(3)`
`=(a+b+c)|(1,1,b+c),(1,1,c+a),(1,1,a+b)|=0`
`because " two columns are same so value of determinant is zero."`
3. `|(0,c,b),(-c,0,a),(-b,-a,0)|=0`
`because" diagonal is zero so value of determinant is zero."`
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