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If `A=[1 0 2 0 2 1 2 0 3]` , prove that `A^3-6A^2+7A+2I=0`

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NCERT GUJARATI-MATRICES-EXERCISE 3.2
  1. Compute the indicated products: (i) [(a,b),(-b,a)][(a,-b),(b,a)] (i...

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  2. if A=[{:(1,2,-3),(5,0,2),(1,-1,1):}],B=[{:(3,-1,2),(4,2,5),(2,0,3):}]a...

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  3. A=[[2/3,1,5/3],[1/3,2/3,4/3],[7/3,2,2/3]] and B=[[2/5,3/5,1],[1/5,2/5,...

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  4. Show that costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sint...

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  5. 2X+3Y=[[2,3],[4,0]] and 3X+2Y=[[2,-2],[-1,5]]

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  6. Find X, if Y=[3 2 1 4]and 2X+Y=[1 0-3 2]

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  7. Find the values of x and y, if 2[{:(1,3),(0,x):}]+[{:(y,0),(1,2) :}]...

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  8. Find x ,\ y ,\ z ,\ t if 2[x z y t]+3[1-1 0 2]=3[3 5 4 6] .

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  9. ifx[{:(2),(3):}]+Y[{:(-1),(1):}]=[{:(10),(5):}],find the values of X ...

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  10. Given 3[x y z w]-[x6-1 2w]+[4x+y z+w3] , find the values of x, y, z an...

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  11. If F(x) =[(cos x, -sin x,0),(sin x,cos x,0),(0,0,1)] show that F(x)F(y...

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  12. show that (i) [{:(5,-1),(6,7):}][{:(2,1),(3,4):}]ne[{:(2,3),(3,4):}...

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  13. Find A^2-5A+6I , if A=[2 0 1 2 1 3 1-1 0]

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  14. If A=[1 0 2 0 2 1 2 0 3] , prove that A^3-6A^2+7A+2I=0

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  15. If A A=[3-2 4-2]and I=[1 0 0 1], find k so that A^2=k A-2I.

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  16. Let A=[0-tan(alpha//2)tan(alpha//2)0] and I be the identity matrix ...

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  17. A trust fund has Rs 30,000 that must be invested in two different t...

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  18. The bookshop of a particular school has 10 dozen chemistry books, 8...

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  19. Assume X, Y, Z, W and P are matrices of order 2 xxn , 3 xxk , 2 xxp...

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  20. Assume X, Y, Z, W and P are matrices of order 2 xxn , 3 xxk , 2 xxp...

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