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Prove that: |1a a^2-b c1bb^2-c a1cc^2-a ...

Prove that: `|1a a^2-b c1bb^2-c a1cc^2-a b|=0`

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Prove that det[[1,a,a^(2)-bc1,b,b^(2)-ca1,c,c^(2)-ab]]=0

Without expanding, show that the value of each of the determinants is zero: |1/a a^2b c a/bb^2a c a/cc^2a b|

Without expanding prove that: |[1,a,a^(2)-bc],[1,b,b^(2)-ca],[1,c,c^(2)-ab]|=0

By using properties of determinants. Show that: (i) |1a a^2 1bb^2 1cc^2|=(a-b)(b-c)(c-a) (ii) |1 1 1a b c a^3b^3c^3|=(a-b)(b-c)(c-a)(a+b+c)

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

Prove that |{:(1, a, a^(2)-bc),(1, b, b^(2)-ca), (1, c, c^(2)-ab):}|=0

If a b+b c+c a=0 , then what is the value of (1/(a^2-b c)+1/(b^2-c a)+1/(c^2-a b)) ? (a) 0 (b) 1 (c) 3 (d) a+b+c

Prove that |[1,1,1] , [a,b,c] ,[a^2-bc, b^2-ca, c^2-ab]|=0

Without expanding the determinant , prove that |{:(a, a^(2),bc),(b,b^(2),ca),(c,c^(2),ab):}|=|{:(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3)):}|

ALLEN-DETERMINANTS-All Questions
  1. Comprehension 2 Consider the system of linear equations alphax+y...

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  2. Without expanding the determinant prove that: |0b-c-b0a c-a0|=0

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  3. Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

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  4. Prove that: |a^2+2a2a+1 1 2a+1a+2 1 3 3 1|=(a-1)^3 .

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  5. By using properties of determinants. Show that:|1+a^2-b^2 2a b-2b2a b1...

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  6. Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot

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  7. Absolute value of sum of roots of the equation |x+22x+3 3x+4 2x+3 3x+4...

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  8. a+b+c=0, solve for x : [[a-x,c,b],[c,b-x,a],[b,a,c-x]]=0

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  9. Prove that '[[b-c,c-a,a-b],[b'-c'],[c'-a'][a'-b'],[b"-c",c"-a",a"-b"]]...

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  10. If 3 digit numbers A28, 3B9 and 62C are divisible by a fixed constant ...

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  11. For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)...

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  12. If Dr=|2^(r-1)2(3^(r-1))4(5^(r-1))x y z2^n-1 3^n-1 5^n-1| then p...

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  13. If D=|[1/z,1/z,-(x+y)/(z^2)],[-(y+z)/(x^2),1/x,1/x],[-(y(y+z)/(x^2z))...

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  14. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

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  15. Solve the following sets of equations using Cramer's rule and remark a...

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  16. Solve the following sets of equation using Cramers rule and remark ...

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  17. Solve the following sets of equation using Cramers rule and remark ...

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  18. . For what values of lambda and mu the system of equations x+y+z=6, x+...

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  19. Find those values of c for which the equations: 2x+3y=3,(c+ 2)x + (c +...

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  20. Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system...

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