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" If " Delta(1) =|{:(x,,b,,b),(a,,x,,b)...

`" If " Delta_(1) =|{:(x,,b,,b),(a,,x,,b),(a,,a,,x):}|" and " Delta_(2)= |{:(x,,b),(a,,x):}|` are the given determinants then

A

`Delta_(1) = 3 (Delta_(2))^(2)`

B

`(d)/(dx) (Delta_(1)) = 3 Delta_(2)`

C

`(d)/(dx) (Delta_(1)) = 3 Delta_(2)^(2)`

D

`Delta_(1) = 3 (Delta_(2))^(3//2)`

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise
  1. The determinant D=|{:(cos(alpha+beta),-sin(alpha+beta),cos2beta),(sina...

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  2. If omega is a cube root of unity, then Root of polynomial is |(x + 1...

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  3. " If " Delta(1) =|{:(x,,b,,b),(a,,x,,b),(a,,a,,x):}|" and " Delta(2)...

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  4. If y= sin px and y(n) is the nth derivative of y, then |{:(y,y(1),y(...

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  5. If |p b c a q c a b r|=0 , find the value of p/(p-a)+q/(q-b)+r/(r-c),\...

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  6. Using properties of determinants, show that |{:(x, p, q), ( p, x, q)...

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  7. The factors of |(x,a,b),(a,x,b),(a,b,x)|, are

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  8. Let omega=-1/2+i(sqrt(3))/2dot Then the value of the determinant |1 1 ...

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  9. If a+b+c=0, one root of |a-x c b c b-x a b a c-x|=0 is x=1 b. x=2 c. ...

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  10. suppose D= |{:(a(1),,b(1),,c(1)),(a(2),,b(2),,c(2)),(a(3),,b(3),,c(3...

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  11. A and B are two non-zero square matrices such that AB = O. Then,

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  12. The roots of the equation |{:(x-1,1,1),(1,x-1,1),(1,1,x-1):}|=0 are

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  13. From the matrix equation AB=AC, we conclude B=C provided.

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  14. If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]| , B=|[1,bc, a],[1,ca, b],[1,...

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  15. The value of |(11,12,13),(12,13,14),(13,14,15)|, is

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  16. |{:(x,4, y+z),(y,4,z+x),(z,4,x+y):}| is equal to:

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  17. If f(x)=|{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}|, then

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  18. Let a ,b , c be the real numbers. The following system of equations in...

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  19. A ,\ B are two matrices such that A B and A+B are both defined; sho...

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  20. If omega is an imaginary cube root of unity, then the value of |(a,b o...

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