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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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By using properties of determinants. Show that: |[1+a^2-b^2, 2a b,-2b],[2a b,1-a^2+b^2, 2a],[2b,-2a,1-a^2-b^2]|=(1+a^2+b^2)^3

Using properties of determinants, prove 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)

Using properties of determinants, show that |1 a a^2 -b c 1 b b^2 -c a 1 c c^2 -a b|=0

By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)

Using properties of determinant, prove that |(2a, a-b-c, 2a), (2b, 2b, b-c-a), (c-a-b,2c,2c)|=(a+b+c)^(3) .

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

Using properties of determinants prove that |(2ab,a^(2),b^(2)),(a^(2),b^(2),2ab),(b^(2),2ab,a^(2))|=-(a^(3)+b^(3))^(2) .

Using properties of determinant : Prove that |(a^(2), 2ab, b^(2)),(b^(2),a^(2),2ab),(2ab,b^(2),a^(2))| = (a^(3) + b^(3))^(2)

Using the properties of determinants, prove that following |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c)^3

Using properties of determinant prove that |(a^(2)+1, ab, ac),(ab, b^(2)+1, bc),(ca, cb,c^(2)+1)|=(1+a^(2)+b^(2)+c^(2)) .

ALLEN-DETERMINANTS-All Questions
  1. Using properties of determinants, evaluate |[18, 40 ,89],[ 40 ,89, 198...

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  2. Find the area of the triangle with vertices at the points: (-1 ,-8 ), ...

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

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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) .

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  5. Absolute value of sum of roots of the equation |[x+2,2x+3, 3x+4],[ 2x+...

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  6. If a+b+c=0, one root of |a-x c b c b-x a b a c-x|=0 is x=1 b. x=2 c. ...

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  7. Prove that |b+c a a b c...

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  8. about to only mathematics

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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 "Delta"r=|[2^(r-1),2. 3^(r-1),4. 5^(r-1)],[x, y ,z],[2^n-1, 3^n-1, ...

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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. about to only mathematics

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  13. Solve the following sets of equation using Cramer’s rule and remark...

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

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  15. Determine for that values of lambda and mu the following system of eq...

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

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  17. Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...

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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. Using the properties of determinants, find the value of | 0 a -b ...

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