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Without expanding as far as possible, pr...

Without expanding as far as possible, prove that
`|{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}|`=(x-y)(y-z)(z-x)(x+y+z).

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MOTION-DETERMINANTS -EXERCISE-3
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  2. The parameter on which the value of the determinant |1a a^2"cos"(p-d)x...

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  3. Without expanding as far as possible, prove that |{:(1,1,1),(x,y,z),...

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  4. |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|

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  5. |[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...

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  6. Prove that |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=(a+b+c)(a^(2)+b^(2)...

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  7. Show that the value of the determinant |(tan(A+Q),tan(B+P),tan(C+P)),...

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

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  9. Solve for x, |[x+2,2x+3,3x+4] , [2x+3,3x+4,4x+5] , [3x+5,5x+8, 10x+17]...

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  10. Solve : |x-2 2x-3 3x-4x-4 2x-9 3x-16 x-8 2x-27 3x-64|=0

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  11. If a + b + c = 0 one root of |(a -x,c,b),(b,b -x,a),(b,a,c -x)|= 0, is

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  12. 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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  13. 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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  14. Show that | [a^2 +lambda, ab, ac], [ab, b^2+lambda, bc], [ac, bc, c^2+...

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

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

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

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

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

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