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Show that |{:(a+b+2c,a,b),(c,b+c+2a,b),...

Show that `|{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3`

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1B MCQ (DETERMINANTS)
  1. |(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ac,bc,c^(2)+1)|=

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  2. Show that |{:(a-b-c," "2a," "2a),(" "2b,b-c-a," "2b),(" "2c," "2...

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  3. Show that |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3

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  4. A=[(1, 5, 6),(2,3,4),(1,1,1)] find rank of A

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  5. |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=

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

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  7. |(a^(2)+2a,2a+1,1),(2a+1,a+2,1),(3,3,1)|

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  8. |(sin^(2)x,cos^(2)x,1),(cos^(2)x,sin^(2)x,1),(-10,12,2)|=

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  9. If A=[a(ij)] is a scalar matrix of order nxxn such that a(ij)=k for al...

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  10. If A=[a(ij)] is a square matrix of order nxxn and k is a scalar then |...

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  11. |(x,p,q),(p,x,q),(p,q,x)|=

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  12. Prove that |{:(y+z,x,x),(y,z+x,y),(z,z,x+y):}|=4xyz

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  13. |(a+b,c,c),(b,a+c,b),(a,a,b+c)|=

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

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  15. If |((a^(2)+b^(2))//c, c, c),(a,(b^(2)+c^(2))//a,a),(b,b,(c^(2)+a^(2))...

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  16. |((b+c)^(2),a^(2),a^(2)),(b^(2),(c+a)^(2),b^(2)),(c^(2),c^(2),(a+b)^(2...

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

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  18. IfA=[(1,-2,0),(5,2,3),(1,1,x)] and det(A)=3 Find x=

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  19. If |(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2))|=k the...

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  20. Prove that |{:(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a...

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