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By using properties of determinants. Sho...

By using properties of determinants. Show that:`|1+a^2-b^2 2a b-2b2a b1-a^2+b^2 2a2b-2a1-a^2-b^2|=(1+a^2+b^2)^3`

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1+a^(2)-b^(2),2ab,-2b2ab,1-a^(2)+b^(2),2a2b,-2a,1-a^(2)-b^(2)]|=(1+a^(2)+b^(2))^(3)

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)

By using properties of determinants.Show that: det[[a^(2)+1,ab,acab,b^(2)+1,bcca,cb,c^(2)+1]]=(1+a^(2)+b^(2)+b^(2))

|[1+a^(2)-b^(2),2ab,-2b],[2ab,1-a^(2)+b^(2),2a],[2b,-2a,1-a^(2)-b^(2)]| =

a a+b a+2b 10. Using properties of determinants, show that |[a,a+b,a+2b],[a+2b,a,a+b],[a+b,a+2b,a]|=9b^2(a+b)

Find the value |{:(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2)):}|

Show that |{:(1+a^(2)-b^(2),,2ab,,-2b),(2ab,,1-a^(2)+b^(2),,2a),(2b,,-2a,,1-a^(2)-b^(2)):}| = (1+a^(2) +b^(2))^(3)

The value of the determinant |{:(1+ a^(2) - b^(2),2 ab , - 2b),(2ab, 1 - a^(2) + b^(2), 2a),(2b , -2a , 1-a^(2) - b^(2)):}| is equal to

Solve the determinant using properties |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]| = (a+b+c)^3

If (a+b):(a-b)=1:5 then (a^2-b^2):(a^2+b^2)=

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

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

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

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

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

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

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

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

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  10. 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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  11. 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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  12. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

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

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

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

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

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

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

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  19. 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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  20. If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...

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