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Prove that: |{:(a, b, c), (x, y, z), (...

Prove that: `|{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, a, p), (z, c, r):}|`

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If A = |(a,b,c),(x,y,z),(p,q,r)| and B = |(q,-b,y),(-p,a,-x),(r,-c,z)| , then

If A=[(a, b, c), (x, y, z), (p, q, r)], B=[(q,-b, y),(-p, a,-x),(r,-c, z)] and if A is invertible, then which of the following is not true? (a) |A|=|B| (b) |A|=-|B| (c) |adj A|=|adj B| (d) A is invertible if and only if B is invertible

If |{:(a-b,b-c,c-a),(x-y,y-z,z-x),(p-q,q-r,r-p):}|=m|{:(c,a,b),(z,x,y),(r,p,q):}|," then m"=

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

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Using properties of determinants, prove that |(b+c,q+r,y+z),(c+a,r+p,z+x),(c+b,p+q,x+y)|=2|(a,p,x),(b,q,y),(c,r,z)|

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If Delta_1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta_2=|[q,-b, y],[-p, a,-x],[ r,-c, z]|, without expanding or evaluating Delta_1 and Delta_2 , show that Delta_1+Delta_2=0

Using the property of determinants and without expanding, prove that: |[b+c, q+r, y+z],[ c+a, r+p, z+x],[ a+b, p+q, x+y]|=2|[a, p, x],[ b, q ,y],[ c, r, z]|

ALLEN-DETERMINANTS-All Questions
  1. The value of |{:(1, 2, 3),(-4, 3, 6),( 2,-7, 9):}| is a.213 b.-231 c...

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  2. Find the minors and cofactors of elements '-3^(prime),\ \ ^(prime)5^(p...

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  3. Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, ...

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

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

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

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

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

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

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

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

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

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

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

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

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  17. 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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  18. 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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  19. The number of real values of x satisfying |(x,3x+2,2x-1),(2x-1,4x,3x+1...

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

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