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If A=[[2,0,-1],[5,1,0],[0,1,3]], prove t...

If `A=[[2,0,-1],[5,1,0],[0,1,3]]`, prove that : `A^-1=A^2-6A+11I`

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MODERN PUBLICATION-MOCK TEST-3-EXERCISE
  1. Solve: tan^-1 2x + tan^-1 3x = frac{pi}{4}

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  2. If A=[[2,-1],[-1,2]],show that A^2-4A+3I=0.

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  3. If A=[[2,0,-1],[5,1,0],[0,1,3]], prove that : A^-1=A^2-6A+11I

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  4. Without expanding, prove the following |(b+c,c+a,a+b),(q+r,r+p,p+q)...

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  5. If the function defined by : f(x) = {:{(2x-1,x<2),(a,x=2),(x+1,x>2):...

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  6. Differentiate the following w.r.t.x. x^(cot x) + (sin x)^x.

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  7. Evalute : int(5x+3)/sqrt(x^2+4x+10)dx

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  8. Evaluate : int0^pi (xsinx)/(1+cos^2x)dx.

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  9. Evaluate : ∫0^(pi/2)frac{cos^2x}{cos^2x+4sin^2x}dx

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  10. For the differential equation, find the particular solution satisfying...

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  11. Find the vector equation of the line parallel to the line : (x-1)/5=(3...

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  12. Find the equation of the plane passing through the point ( 1, -1 , 2) ...

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  13. A speaks truth in 60% of the cases, while B in 90% of the cases. In wh...

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  14. Consider f: Rrarr [- 5, ∞) given by f(x) = 9x^2 + 6x- 5. Show that f i...

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  15. Consider the binary operations * : R xx R to R and o: R xx R to R def...

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  16. Show that a cylinder of given volume, open at the top, has minimum tot...

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  17. Using integration find the area of region bounded by the triangle wher...

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  18. Show that the points : A(-2hati+3hatj+5hatk), B(hati+2hatj+3hatk) and ...

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  19. Show that the lines (x-a+d)/(alpha-delta) = (y-a)/alpha = (z-a-d)/(alp...

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  20. Two tailors A and B earn Rs 150 and Rs 200 per day respectively. A can...

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