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If A is a matrix of order 3, then det(kA...

If A is a matrix of order 3, then `det(kA)` is

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ALLEN-DETERMINANTS-All Questions
  1. Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, ...

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  2. Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a...

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  3. If A is a matrix of order 3, then det(kA) is

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  4. If |{:(3^(2)+k,4^(2),3^(2)+3+k),(4^(2)+k,5^(2),4^(2)+4+k),(5^(2)+k,6^...

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  5. Prove that |{:(a, a, x), (m, m, m), (b, x, b):}|=m(x-a)(x-b)

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  6. Let alpha\ &\ beta be the roots of equation a x^2+b x+c=0\ a n d Sn=al...

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  7. Prove that |1alphaalpha^2alphaalpha^2 1alpha^2 1alpha|=-(1-alpha^3)^2d...

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  8. Find the nature of solution for the given system of equation: x+2y+3...

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  9. Find the value of lambda if the following equations are consistent ...

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  10. If the system of equation x+lambday+1=0,\ lambdax+y+1=0\ &\ x+y+lambda...

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  11. The value of the determinant |[a-b,b+c, a], [b-a, c+a, b], [c-a, a+b...

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  12. If |[sin2x,cos^2x,cos4x],[cos^2x,cos2x,sin^2x],[cos^4x,sin^2x,sin2x]|=...

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  13. The value of the determinant |-a b c a-b c a b-c| is equal to- 0 b. (a...

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  14. For any "Delta"A B C the value of determinant |sin^2\ \ A cot A1sin^2B...

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  15. If Dp=|p 15 8p^2 35 9p^3 25 10|,\ t h e n\ D1+D2+D3+D5 is equal to- a....

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  16. If A+B+C=pi,\ t h e n\ |"sin"(A+B+C)s in B cos C-s in B0t a n A"cos"(A...

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  17. The number of real values of x satisfying |(x,3x+2,2x-1),(2x-1,4x,3x+1...

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  18. If a ,\ b ,\ c are pth, qth and rth terms of a GP, the |loga p1logb q1...

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  19. If a1, a2 an ,\ a(n+1) are in GP and a1>0AAI ,\ t h e n |loganloga(n+2...

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  20. If p x^4+q x^3+r x^2+s x+t=|x^2+3xx-1x+3x+1 2-xx-3x-3x+4 3x| then t is...

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