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Delta= |{:(1,,1+ac,,1+bc),(1,,1+ad,,1+bd...

`Delta= |{:(1,,1+ac,,1+bc),(1,,1+ad,,1+bd),(1,,1+ae,,1+be):}|` is independent of

A

a

B

b

C

c,d,e

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Operating `C_(2) to C_(2)-C_(1),C_(3) to C_(3)-C_(1)` we get
`Delta =|{:(1,,ac,,bc),(1,,ad,,bd),(1,,ae,,be):}|=ab|{:(1,,c,,c),(1,,d,,d),(1,,e,,e):}|= ab (0) =0`
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CENGAGE-DETERMINANTS-All Questions
  1. Delta= |{:(1,,1+ac,,1+bc),(1,,1+ad,,1+bd),(1,,1+ae,,1+be):}| is indepe...

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  2. Statement 1: If b c+q r=c a+r p=a b+p q=-1, t h e n|a p a p b q b q c...

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  3. If f(theta)=|sinthetacosthetasintheta costhetasinthetacostheta costhet...

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  4. If f(theta)=|[sin^2A,cot A,1],[sin^2B,cosB,1],[sin^2C,cosC,1]| , then...

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  5. The roots of the equation |^x Cr^(n-1)Cr^(n-1)C(r-1)^(x+1)Cr^n Cr^n C(...

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  6. Let Delta(x)=|[3,3x,3x^2+2a^2] , [3x, 3x^2+2a^2, 3x^3+6a^2x] , [3x^2+2...

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  7. The determinant "Delta"=|(a^2+x) ab ac ab (b^2+x) bc ac bc (c^2+...

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  8. If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,t h e nf(2x)-f(x) is d...

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  9. If g(x)-(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of d...

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  10. If (x)= |x^2+4x-3 2x+4 13 ...

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  11. If |y z-x^2z x-y^2x y-z^2x z-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|=|...

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  12. Let f (n) = |{:(n,,n+1,,n+2),(.^(n)P(n),,.^(n+1)P(n+1),,.^(n+2)P(n+2)...

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  13. If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e...

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  14. Let x<1, then value of [[x^2+2, 2x+1 ,1],[ 2x+1,x+2, 1],[ 3, 3 ,1]...

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  15. If f (x) = |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|then

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  16. Value of [[x+y, z,z ],[x, y+z, x],[y, y, z+x]], where x ,y ,z are non...

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  17. Which of the following is not the root of the equation |[x,-6,-1],[ 2,...

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  18. If A,B,C are the angles of a non right angled triangle ABC. Then find ...

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  19. If f(x)=|x a a a x a a a x|=0, then f^(prime)(x)=0a n df^(x)=0 has com...

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  20. Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),...

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  21. Roots of the equation |x m n1a x n1a b x1a b c1|=0 are independent of ...

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