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Show that |{:(a,b,c),(b,c,a),(c,a,b):}|^...

Show that `|{:(a,b,c),(b,c,a),(c,a,b):}|^2=|{:(2bc-a^(2),c^(2),b^(2)),(c^(2),2ac-b^(2),a^(2)),(b^(2),a^(2),2ab-c^(2)):}|=(a^(3)+b^(3)+c^(3)-3abc)^(2)`

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Show that |{:(a,b,c),(b,c,a),(c,a,b):}|=|{:(2bc-a^2,c^2,b^2),(c^2,2ac-b^2,a^2),(b^2,a^2,2ab-c^2):}|=(a^3+b^3+c^3-3abc)^2

|((b+c)^(2),a^(2),bc),((c+a)^(2),b^(2),ca),((a+b)^(2),c^(2),ab)|=

|(0,ab^(2),ac^(2)),(a^(2)b,0,bc^(2)),(a^(2)c,b^(2)c,0)|=

Show that |{:(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab):}|=0

Show that |{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(2),b^(3),c^(3)):}|=abc(a-b)(b-c)(c-a)

|(0,c,b),(-c,0,a),(b,a,0)|-|(b^(2)+c^(2),ab,ac),(ab,c^(2)+a^(2),bc),(ac,bc,a^(2)+b^(2))|=

I: |(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2))|=2a^(2)b^(2)c^(2) II: |(0,ab^(2),ac^(2)),(a^(2)b,0,bc^(2)),(a^(2)c,b^(2)c,0)|=2a^(3)b^(3)c^(3)

DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1B MCQ (DETERMINANTS)
  1. |(2bc-a^(2),c^(2),b^(2)),(c^(2),2ca-b^(2),a^(2)),(b^(2),a^(2),2abc-c^(...

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  2. |(0,c,b),(-c,0,a),(b,a,0)|-|(b^(2)+c^(2),ab,ac),(ab,c^(2)+a^(2),bc),(a...

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  3. Show that |{:(a,b,c),(b,c,a),(c,a,b):}|^2=|{:(2bc-a^(2),c^(2),b^(2)),(...

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  4. Prove that |{:((1+ax)^(2),(1+ay)^(2),(a+az)^(2)),((1+bx)^(2),(1+by)^(2...

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  5. A factor o |((a-x)^(2),(b-x)^(2),(c-x)^(2)),((a-y)^(2),(b-y)^(2),(c-y)...

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  6. |(cos (alpha+beta),-sin (alpha+beta),cos 2 beta),(sin alpha, cos alpha...

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  7. |(sin alpha, cos alpha, sin (alpha+delta)),(sin beta, cos beta, sin(be...

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  8. |(cos alpha, sin alpha, cos (alpha+beta)),(- sin alpha, cos alpha, -si...

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  9. |(0, sin alpha, sin beta),(sin alpha, 0, sin gamma),(sin beta, sin gam...

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  10. A=[(1, cos (beta-alpha),cos(gamma-alpha)),(cos (alpha-beta), 1, cos(ga...

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  11. If A+B+C=pi then |(sin^(2)A,cotA,1),(sin^(2)B,cotB,1),(sin^(2)C,cotC,1...

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  12. If A,B,C are th angle of a equilateral DeltaABC, then |(sin2A,sinC,sin...

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  13. For all values of A, B, C and P, Q, R |(cos(A-P), cos(A-Q),cos(A-R))...

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  14. |(x^(3)+x,x+1,x-2),(2x^(3)+3x-1,3x,3x-3),(x^(3)+2x+3,2x-1,2x-1)|=xA+B ...

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  15. If |(lamda^(2)+3lamda, lamda-1, lamda+3),(lamda+1, 2-lamda,lamda-4),(l...

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  16. If |(lamda^(2)+3lamda, lamda-1, lamda+3),(lamda+1, 2-lamda,lamda-4),(l...

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  17. If a^(2)+b^(2)+c^(2)=-2 and f(x)=|(1+a^(2)x,(1+b^(2))x,(1+c^(2))x),((1...

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  18. If f(r)(x),g(r)(x),h(r)(x),r=1,2,3 are polynomials in x such that f(r)...

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  19. If alpha be a repeated root of a quadratic equation f(x) = 0 and A(x)...

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  20. Let the three digit number A28, 3B9,62C, where A,B,C are integers betw...

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