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If |[x,3, 6],[ 3, 6,x],[6,x,3]|=|[2,x,7]...

If `|[x,3, 6],[ 3, 6,x],[6,x,3]|=|[2,x,7],[x,7, 2],[ 7, 2,x]|=|[4, 5,x],[5,x,4],[x,4, 5]|=0,` then `x` is equal to a.`0` b. `-9` c. `3` d. none of these

A

0

B

-9

C

3

D

none of these

Text Solution

Verified by Experts

In each determinant applying `R_(1) to R_(1)+R_(2)+R_(3)` and then taking out `(x+9)` common we get
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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Consider the set A of all determinants of order 3 with entries 0 or 1 ...

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  2. Solve: |[x^2-1, x^2+2x+1, 2x^2+3x+1], [2x^2+x-1, 2x^2+5x-3, 2x^2+4x-3...

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  3. If |[x,3, 6],[ 3, 6,x],[6,x,3]|=|[2,x,7],[x,7, 2],[ 7, 2,x]|=|[4, 5,x]...

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  4. If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...

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  5. If f^(prime)(x)=|[mx, mx-p, m x+p], [n, n+p, n-p], [mx+2n, m x+2n+p, m...

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  6. If sum(n=1)^nalphan=a n^2+b n ,w h e r ea ,b are constants and alpha...

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  7. The determinant |[x p+y, x, y], [y p+z, y, z],[0,x p+y, y p+z]|=0...

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  8. Using properties of determinant prove that |[a+b+c,-c,-b],[-c, a+b+c,...

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  9. Show that |^x Cr^x C(r+1)^x C(r+2)^y Cr^y C(r+1)^y C(r+2)^z Cr^z C(r+1...

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  10. If omega!=1 is a cube root of unity and x+y+z!=0, then prove that |[x/...

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  11. Statement 1: If the system of equation lambdax+(b-a)y+(c-a)z=0,(a-b)x+...

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  12. If A , Ba n dC are the angels of a triangle, show that |[-1+cos B, c...

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  13. If alpha,beta,gamma are the angles of a triangle and system of equatio...

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  14. Without expanding the determinants, prove that |(103, 115, 114), (111,...

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  15. Given a=x//(y-z), b=y//(z-x), and c=z//(x-y),w h e r e .x , y and z a...

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  16. Find the value of determinant |[sqrt((13))+sqrt(3),2sqrt(5),sqrt(5)],[...

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  17. If the lines ax+y+1=0, x+by+1=0, x+y+c=0, (a, b, c are distinct and no...

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  18. Prove that the value of the determinant |[-7, 5+3i,2/3-4i], [5-3i,8, 4...

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  19. If the system of linear equation x+y+z=6,x+2y+3c=14 , and 2x+5y+lambda...

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  20. If ar=(cos2rpi+i sin 2rpi)^(19) , then prove that |[a1,a2,a3],[a4,a5,a...

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