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

Show that `A=|{:(-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c):}|=4(a+b)(b+c)(c+a)`

A

`4(a+b)(b+c)(c+a)`

B

`(a-b)(b-c)(c-a)`

C

`4(a+b+c)`

D

`4(ab+bc+ca)`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-MATRICES -DETERMINANTS- EXERCISE - II
  1. If a,b,c are positive and not all equal then |(a,b,c),(b,c,a),(c,a,b)|

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

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  3. Show that A=|{:(-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c):}|=4(a+b)(b+c...

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  4. If a+b+c=0 and |(a-x,c,b),(c,b-x,a),(b,a,c-x)|=0 then x=

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  5. If |(lamda^(2)+3lamda, lamda-1, lamda+3),(lamda+1, 2-lamda,lamda-4),(l...

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  6. Let |{:(x^(2)+x+1,x+1,2x-3),(3x^(2)-1,x+2,x-1),(x^(2)+5x+1,2x+3,x+4):}...

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  7. If |(a,b,a alpha+b),(b,c, b alpha+c),(a alpha+b, b alpha+c,0)|=0 then

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  8. If a,b,c are the p^(th),q^(th),r^(th) terms in H.P. then |{:(bc,p,1),(...

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  9. If |(3x-8,3,3),(3,3x-8,3),(3,3,3x-8)|=0 then x=0

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  10. If a,b,c are different and |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 the...

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  11. If x=-1 is a root of the equation |{:(2-x,3,3),(3,4-x,5),(3,5,4-x):}|=...

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  12. If one of the roots of |(3,5,x),(7,x,7),(x,5,3)|=0 is -10, then the ot...

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  13. If |(x,x+y,x+y+z),(2x,3x+2y,4x+3y+2z),(3x,6x+3y,10x+6y+3z)|=64 then x=

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  14. If a,b,c, are in A.P. then |(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c)|...

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  15. If a,b,c are pth, qth rth terms respectivelyy of a G.P then |(loga, p,...

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  16. If |{:(0,sinalpha,sinbeta),(sinalpha,0,singamma),(sinbeta,singamma,0):...

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  17. With the usual notation in DeltaABC det|(1,1,1),(sinA,sinB,sinC),(sin^...

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  18. If y=cosx,y(n)=(d^(n)(cosx))/(dx^(n)) then |{:(y(4),y(5),y(6)),(y(7),y...

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  19. If |{:(cos(A+B),-sin(A+B),cos2B),(sinA,cosA,sinB),(-cosA,sinA,cosB):}|...

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  20. A=[(1, cos (beta-alpha),cos(gamma-alpha)),(cos (alpha-beta), 1, cos(ga...

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