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If A=[[alpha,0],[1,1]] and B=[[1,0],[5,1...

If `A=[[alpha,0],[1,1]]` and `B=[[1,0],[5,1]]`, show that for no values of `alpha, A^2=B`.

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MODERN PUBLICATION-TEST PAPER 10-EXERCISE
  1. Solve x + 2y = 3, 3x + y = 4 by matrix method.

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  2. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

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  3. If A=[[alpha,0],[1,1]] and B=[[1,0],[5,1]], show that for no values of...

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  4. Prove that |(1, a, a^3),(1, b, b^3),(1, c, c^3)|= (a-b)(b-c)(c-a)(a+b+...

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  5. If x^7y^3=(x+y)^10, then find (d^2y)/(dx^2)

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  6. If tangents are drawn from the origin to the curve y = sin x, then sho...

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  7. Integrate the following int(3x+4)/(xsqrt(2x^2-5))dx

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  8. Evaluate int(0)^(4)(x+e^(2x))dx, as limit of sum.

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  9. Solve : (dy)/(dx)= sin(x+y)+cos(x+y)

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  10. Solve the following differential equations (1-x^2)(dy)/(dx)+2xy= x s...

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  11. If vec a, vec b, vec c are mutually perpendicular vectors of equal mag...

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  12. Prove that the lines joining the midpoints of consecutive sides of a q...

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  13. int0^1(x^5(4-x^2))/sqrt(1-x^2)dx

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  14. find the point of intersection of the line through (1,3,-2) and (3,4,1...

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  15. Prove that the lines frac[x+3][2]=frac[y+5][3]=frac[z-7][-3] and frac[...

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

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  17. Show that f : A to B, where A=R - {3}, B=R - {1} defined as f(x)=(x-2)...

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  18. Find the particular solution of the differential equation dy/dx+y cot ...

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  19. Prove that the curves y^(2)=4x and x^(2)=4y divide the area of the squ...

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  20. A line with direction ratios lt2,1,2gt meets each of the lines x=y+a=z...

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