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Show that | [a^2 +lambda, ab, ac], [ab, ...

Show that `| [a^2 +lambda, ab, ac], [ab, b^2+lambda, bc], [ac, bc, c^2+lamda]|` is divisible by `lambda^2` and find the other factor

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`lambda^(2)(a^(2)+b^(2)+c^(2)+lambda)`
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MOTION-DETERMINANTS -EXERCISE-3
  1. 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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  2. If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-...

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  3. Show that | [a^2 +lambda, ab, ac], [ab, b^2+lambda, bc], [ac, bc, c^2+...

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  4. Prove that :|[a^2,b^2,c^2], [(a+1)^2, (b+1)^2, (c+1)^2], [(a-1)^2, (b-...

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  5. In triangle A B C , if |1 1 1cotA/2cotB/2cotC/2tanB/2+tanC/2tanB/2+tan...

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  6. Prove that |{:(2,alpha+beta+gamma+delta,alphabeta +gammadelta),(alph...

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  7. Solve for x the equation |(a^(2),a,1),(sin(n+1)x,sin nx,sin(n-1)x),(...

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

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

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

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  11. For what value of K do the following system of equations poss...

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  12. Investigate for what values of lambda, mu the simultaneous equa...

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  13. Investigate for what values of lambda, mu the simultaneous equa...

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

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  15. If the system of equations x – ky – z = 0, kx – y – z=0, x + y – z = 0...

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  16. Find the real values of r for which the following system of linear equ...

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

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  18. Ifthe equations a(y +z) =x , b(z+x) = y , c (x + y) = z have nontriv...

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  19. Given a=x//(y-z), b=y//(z-x),a n dc=z//(x-y),w h e r ex , y , za n dz ...

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  20. If sinq!=cosq and x,y,z satisfies the following three equations then f...

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