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Prove that: (i) |{:(,1,1,1),(,a,b,c),(,...

Prove that: (i) `|{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b-c)(c-a)(a+b+c)`

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RESONANCE-MATRICES & DETERMINANT-SECTION-B
  1. If minor of three-one element (i.e.M(31)) in the determinant [{:(,0,1,...

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  2. Using the properties of detminants, evalulate. (i) |{:(,23,6,11),(,36...

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  3. Prove that: (i) |{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b-...

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  4. If a,b,c are positive and ar the p^(th),q^(th),r^(th) terms respective...

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  5. Find the non-zero roots of the equation. (i) Delta=|{:(,a,b,ax+b),(,...

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

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  7. The value of |(a(1) x(1) + b(1) y(1),a(1) x(2) + b(1) y(2),a(1) x(3) +...

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  8. If [{:(,e^(x),sin x),(,cos x,ln(1+x))]:}=A+Bx+Cx^(2)+....... then find...

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  9. If A and B are squar matrices of order 3 such that |A|=-1, |B|=3 then ...

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  10. Let A=[(cos^(- 1)x,cos^(- 1)y,cos^(- 1)z),(cos^(- 1)y,cos^(- 1)z,cos^...

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  11. |[-1,2,1] , [3+2sqrt2,2+2sqrt2,1] , [3-2sqrt2,2-2sqrt2,1]|=

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  12. If alpha,beta & gamma are the roots the equations x^(3)+px+q=0 then th...

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  13. If a, b,c gt 0& x,y,z in R" then the determinant"[{:(,(a^(x)+a^(-x))^(...

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  14. If a,b,c are non-zero real numbers then D=|[b^2 c^2, bc, b+c] , [c^2a^...

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  15. The determinant |(b(1)+c(1),c(1)+a(1),a(1)+b(1)),(b(2)+c(2),c(2)+a(2...

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  16. If x,y,z in R & Delta =|(x,x+y,x+y+z),(2x,5x+2y,7x+5y+2z),(3x,7x+3y,9x...

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  17. The value of the determinant |(cos(theta+phi),-sin(theta+phi),cos2phi)...

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  18. Consider the set A of all determinants of order 3 with entries 0 or 1 ...

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