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

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

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det[[ Prove that :,c^(2)a^(2),b^(2),c^(2)(a+1)^(2),(b+1)^(2),(c+1)^(2)(a-1)^(2),(b-1)^(2),[c-1)^(2)]]=4det[[a^(2),b^(2),c^(2)a,b,c1,1,1]]

[[a^(2),b^(2),c^(2)(a+1)^(2),(b+1)^(2),(c+1)^(2)(a-1)^(2),(b-1)^(2),(c-1)^(2)]]=k[[a^(2),b^(2),c^(2)a,b,c1,1,1]]

|[a^(2), b^(2), c^(2)], [(a+1)^(2), (b+1)^(2), (c+1)^(2)], [(a-1)^(2), (b-1)^(2), (c-1)^(2)]| =-4(a-b)(b-c)(c-a)

Prove that |[1,1,1] , [a,b,c] ,[a^2-bc, b^2-ca, c^2-ab]|=0

If a, b, c are sides of a triangle and |(a^2,b^2,c^2),((a+1)^2,(b+1)^2,(c+1)^2),((a-1)^2,(b-1)^2,(c-1)^2)|= then

a^(2),b^(2),c^(2)(a+1)^(2),(b+1)^(2),(c+1)^(2)(a-1)^(2),(b-1)^(2),(c-1)^(2) then find the value of k

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

Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

MOTION-DETERMINANTS -EXERCISE-3
  1. 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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  2. Show that | [a^2 +lambda, ab, ac], [ab, b^2+lambda, bc], [ac, bc, c^2+...

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

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

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

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

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  8. Solve the following sets of equation using Cramers 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. For what value of K do the following system of equations poss...

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

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

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

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

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

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

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

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

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  20. If f(x)=|(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)...

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