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Without expanding prove that |[1,a,a^(2)...

Without expanding prove that `|[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(2),-ab]|=0`

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

Show that without expanding at any stage |{:(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab):}|=0

Without expanding the determinants prove that |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}| = |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

Without expanding prove abs((bc, a, a^2),(ca, b, b^2),(ab, c, c^2))=abs((1, a^2, a^3),(1, b^2, b^3),(1, c^2, c^3))

Prove without expanding that |[bc,a,a^2],[ca,b,b^2],[ab,c,c^2]|=|[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

Evaluate [[a,a^2-bc,1],[b,b^2-ac,1],[c,c^2-ab,1]]

Without expanding show that |{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]] =0

Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

MODERN PUBLICATION-TEST PAPER 4-PROBLEM
  1. Let A and B be sets. Show that f : A xx B rarr B xx A such that f (...

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  2. (Allocation Problem.)A farmer has 5 acres of land on which he wishes t...

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  3. Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(...

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  4. Prove that abs((a,b,c),(a^2,b^2,c^2),(bc,ca,ab))=(a-b)(b-c)(c-a)(ab+bc...

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  5. If A=[[1,2,3],[3,-2,1],[4,2,1]]"show that"A^3-23A-40I=0

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  6. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

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  7. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

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  8. Show that 2 sin x + than x ge 3x all x in (0, pi/20).

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  9. Prove that the curves x = y^(2) and xy = k cut at right angles, if 8k^...

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  10. Evaluate the following integrals int(dx)/(sinx(3+2cosx) put cosx=z

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  11. int0^(pi//2)(sqrttanx+sqrtcotx)dx

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  12. Determine the area of the region bounded by y^2=x^3 and the double ord...

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  13. Vectors vec(a), vec(b) and vec(c) are such that vec(a) + vec(b) + vec(...

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  14. If l(1), m(1), n(1) and l(2), m(2), n(2)  are the direction cosines of...

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  15. Find the equation of the plane Which contains the line of intersection...

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  16. Find the distance of the point (-1,-5,-10) from the point of intersect...

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  17. Let R be the relation on the set R of real numbers such that aRb iff a...

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  18. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

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  19. Find the minimum distance of a point on the curve 2/x^2+1/y^2= 1 from...

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  20. A variable plane meets the coordinate axes at A, B, C and is at a cons...

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