If A=[(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc...

If `A=[(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,c^(2))]` and `a^(2)+b^(2)+c^(2)=1`, then `A^(2)=`

A

2A

B

A

C

3A

D

`1/2`A

Text Solution

Verified by Experts

The correct Answer is:

B

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Prove that {:[( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2) +bc,c^(2)) ]:} =4a^(2) b^(2) c^(2)

If A=[(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,c^(2))], B=[(0,c,-b),(-c,0,a),(b,-a,0)] then AB=

Knowledge Check

|(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2))|=

A

`a^(2)b^(2)c^(2)`

B

`2a^(2)b^(2)c^(2)`

C

`3a^(2)b^(2)c^(2)`

D

`4a^(2)b^(2)c^(2)`

|(a^(2)+x,ab,ac),(ab,b^(2)+x,bc),(ac,bc,c^(2)+x)|

A

`a^(2)+b^(2)+c^(2)+x`

B

`(a^(2)+b^(2)+c^(2)+x)x^(3)`

C

`(a^(2)+b^(2)+c^(2)+x)x^(3)`

D

none

|(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ac,bc,c^(2)+1)|=

A

`1+a+b+c`

B

`1+a^(2)+b^(2)+c^(2)`

C

`abc+ab+bc+ca`

D

none

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I: |(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2))|=2a^(2)b^(2)c^(2) II: |(0,ab^(2),ac^(2)),(a^(2)b,0,bc^(2)),(a^(2)c,b^(2)c,0)|=2a^(3)b^(3)c^(3)

|(b^(3)+c^(2),ab,ac),(ab,c^(2)+a^(2),bc),(ca,bc,a^(3)+b^(2))|=

|(1//a,a^(2),bc),(1//b,b^(2),ca),(1//c,c^(2),ab)|=

|(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab)|=

|((a+b)^(2),ca,bc),(ca,(b+c)^(2),ab),(bc,ab,(c+a)^(2))|=

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