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Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,...

Prove that `|{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(x-y) (y-z) (z-x) (xy+yz+zx)`

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Show that |{:(1,x, x ^(3)),(1,y,y ^(3)),(1,z,z^(3)):}| = (x-y) (y-z) (z-x) (x + y + z)

Show that: |[x, y ,z],[x^2, y^2, z^2], [yz, zx, xy ]|=(x-y)(y-z)(z-x).(xy+yz+zx)

using the properties of determinants prove that |{:(1,x+y,x^2+y^2),(1,y+z,y^2+z^2),(1,z+x,z^2+x^2):}|=(x-y)(y-z)(z-x)

IF Delta=|{:(1,x,x^2),(1,y,y^2),(1,z,z^2):}| and Delta_1=|{:(1,1,1),(yz,zx,xy),(x,y,z):}| then prove that Delta +Delta_1=0

Show that Delta =Delta_1 where Delta=|{:(Ax,x^2,1),(By,y^2,1),(Cz,z^2,1):}|,Delta_1=|{:(A,B,C),(x,y,z),(zy,zx,xy):}|

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Using properties of determinants, prove that |{:(y^2z^2,yz,y+z),(z^2x^2,zx,z+x),(x^2y^2,xy,x+y):}|=0

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SHARAM PUBLICATION-QUESTION PAPER 2012-EXERCISE
  1. Find the solutions of the following differential equations : y^(2)+x...

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  2. Solve the following differential equations x log x (dy)/(dx)+y= 2 lo...

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  3. Find a vector vec(b) such that vec(a) xx vec(b) = vec(c) and vec(a).ve...

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  4. Prove by vector method that in a Delta ABC, c^(2) = a^(2) + b^(2) - 2a...

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  5. Find the co-ordinates of the point where the perpendicular from the or...

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  6. Solve for x, |{:(15-2x,11,10),(11-3x,17,16),(7-x,14,13):}|=0

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  7. If A=[{:(-1,3,5),(1,-3,-5),(-1,3,5):}], then find A^(3)-A^(2).

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  8. Find the value of the term free from X in the expansion of (3/2(x^(2))...

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  9. A and B are two events. If P(A) = (3)/(8), P(B) = (1)/(2) and P(A nn B...

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  10. If A and B are independent events,show that A^c and B^c are independ...

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  11. Evaluate: underset(x rarr 0)lim ((sinx)/x)

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  12. Integrate: int (sin^(2)x)/(1+cosx)(dx)

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  13. Determine: int sqrt(1+sin2x)dx

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  14. Integrate: int(3x^2)/(x^2+1)dx

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  15. Differentiate sin^(-1)(tanx) with respect to x.

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  16. Prove that the four points (0, 4, 3), (-1, -5, -3), (-2, -2, 1) and (1...

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  17. Show that the lines (x-4)/1=(y+3)/-4=(z+1)/7 and (x-1)/2=(y+1)/-3=(z+1...

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  18. Solve the following LPP graphically Maximize z=20x1+10x2 Subject to x1...

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  19. Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|=|{:(1,1,1),(x^2,y^2,...

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  20. Solve by matrix inversion method. x+y+z=2 2x+y+z=4 x+y-z=1

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