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Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^...

Prove that `|(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|=` `|(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|=2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot`

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Without expanding, show that "Delta"=|(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|=2(a-b)(b-c)(c-a)(x-y)(y-z)(z-x)

Without expanding,FIND "Delta"=|(((a-x)^2),((a-y)^2),((a-z)^2)),(((b-x)^2),((b-y)^2),((b-z)^2)),(((c-x)^2),((c-y)^2),((c-z)^2))|

Prove that : =|{:(1,1,1),(x,y,z),(x^(2),y^(2),z^(2)):}|=(x-y)(y-z)(z-x)

If x+y+z=x y z prove that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/(1-x^2)(2y)/(1-y^2)(2z)/(1-z^2)dot

Prove that |(b+x)(c+x)(v+x)(a+x)(a+x)(b+x)(b+y)(c+y)(c+x)(a+t)(a+y)(b+y)(b+z)(c+z)(c+z)(a+z)(a+z)(b+z)|=(b-c)(c-a)(y-z)(x-y)dot

If x+y+z=xzy , prove that : x(1-y^2) (1-z^2) + y(1-z^2) (1-x^2) + z (1-x^2) (1-y^2) = 4xyz .

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

Multiply : 3a b^2c^3\ b y\ 5a^3b^2c (ii) 4x^2y z\ b y-3/2x^2y z^2

If x/a=y/b=z/c, then show that (x^3+a^3)/(x^2+a^2)+(y^3+b^3)/(y^2+b^2)+(z^3+c^3)/(z^2+c^2)=((x+y+z)^3+(a+b+c)^2)/((x+y+z)^2+(a+b+c)^2).

VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -LEVEL 2
  1. A=[(1,tan x),(-tan x,1)] and f(x) is defined as f(x)= det. (A^(T)A^(-1...

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  2. If A is an idempotent matrix satisfying, (I-0. 4 A)^(-1)=I-alphaA ,w h...

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  3. Let A=[(3x^(2)),(1),(6x)], B=[(a,b,c)], and C=[((x+2)^(2),5x^(2),2x)...

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  4. Let A=[a("ij")](3xx3) be a matrix such that A A^(T)=4I and a("ij")+2c(...

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  5. Let S be the set which contains all possible values of l, m, n, p, q, ...

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  6. Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...

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  7. If a1, a2, a3,54,a6,a7, a8, a9 are in H.P., and D=|[a1,a2,a3],[5, 4,a6...

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  8. about to only mathematics

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  9. The sum of roots of the equations |{:(x+2,,2x+3,,3x+4),(2x+3,,3...

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  10. If alpha,beta,gamma are real numbers, then without expanding at any...

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  11. Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(...

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  12. Express =|2b c-a^2c^2b^2c^2 2c a-b^2a^2b 62a^2 2a b-c^2| as square of ...

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  13. Prove without expansion that |a h+bgga b+c h bf+b afh b+b c af+b cc bg...

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  14. If y= |[sinx,cosx,sinx],[cosx,-sinx,cosx],[x,1,1]|, find (dy)/(dx)

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  15. If f(x)=|x^nn !2cosxcos(npi)/2 4sinxsin(npi)/2 8| then find the val...

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  16. Show that |{:(bc-a^(2),,ca-b^(2),,ab-c^(2)),(ca-b^(2),,ab-c^(2),,bc-a^...

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  17. Write down 2xx2 matrix A which corresponds to a counterclockwise rota...

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  18. If A , B ,a n dC are the angles of triangle, show that the system o...

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  19. If a x1 2+b y1 2+c z1 2=a x2 2+b y2 2+c z2 2=a x3 2+b y3 2+c z3 2=d ,a...

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  20. Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a3b1], [a1b2+a2b1, 2a2b2, a2b3+...

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