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Show that: |a b-cc+b a+c b c-a a-bb+a c|...

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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ALLEN-DETERMINANTS-All Questions
  1. Find the area of the triangle with vertices at the points: (-1 ,-8 ), ...

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

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

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  5. 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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  6. Prove that |b+c a a b c...

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  7. about to only mathematics

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

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  9. 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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  10. 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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  11. about to only mathematics

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

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

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

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

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

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

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

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  20. Find the value of the determinant |"cos"(x-y)"cos"(y-z)"cos"(z-x)"cos"...

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