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Prove that: |a^2+2a2a+1 1 2a+1a+2 1 3 3 ...

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

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ALLEN-DETERMINANTS-All Questions
  1. Without expanding the determinant prove that: |0b-c-b0a c-a0|=0

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

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

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

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

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

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

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

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

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  11. 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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  12. 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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  13. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

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

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

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

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

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

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

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  20. If a^2+b^2+c^2=1 then show that value of the determinant |a^2+(b^2+c^2...

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