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Prove that |{:(y+z,x,x),(y,z+x,y),(z,z,x...

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

A

xyz

B

4xyz

C

2xyz

D

3xyz

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-MATRICES -DETERMINANTS- EXERCISE - II
  1. Show that |{:(x,a,a),(a,x,a),(a,a,x):}|=(x+2a)(x-a)^2

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

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  4. If|(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=k|(a,b,c),(b,c,a),(c,a,b...

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  5. |{:(a-b-c,2b,2c),(2a,b-c-a,2c),(2a,2b,c-a-b):}|=

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  6. If a!=6,b,c satisfy |(a,2b,2c),(3,b,c),(4,a,b)|=0 then abc

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  7. If w is a complex cube root unity then |{:(1,1+w,1+w^(2)),(1+w,1+w^(2)...

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  8. If alpha, beta, gamma are the roots of x^(3)+px+q=0 then |(alpha, beta...

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  9. |(1,log(x)y,log(x)z),(log(y)x,1,log(y)z),(log(z)x,log(z)y,1)|=

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  10. |(1//a,a^(2),bc),(1//b,b^(2),ca),(1//c,c^(2),ab)|=

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  11. Let A=[(5,5 alpha, alpha),(0, alpha, 5 alpha),(0,0,5)] If |A|^(2)=25 t...

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  12. If k gt1, and the determinant of the matrix A^(2), where A=[(k,kalpha,...

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  13. If bc+ca+ab=18, and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=...

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  14. If a,b,c are positive and not all equal then |(a,b,c),(b,c,a),(c,a,b)|

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

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  16. 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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  17. 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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  18. If |(lamda^(2)+3lamda, lamda-1, lamda+3),(lamda+1, 2-lamda,lamda-4),(l...

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

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