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If A=((2,3),(-1,2)).Show that A^(2)-4A+7...

If A=`((2,3),(-1,2))`.Show that `A^(2)-4A+7I=0`whwre I is the unit matrix of order 2.

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PREMIERS PUBLISHERS-MATRICES AND DETERMINANTS-PROBLEMS FOR PRACTICE (ANSWER THE FOLLOWING QUESTIONS)
  1. Find x,y,p,q if[(2x-y,5,5p+2q),(p+2q,x-2y,-10)]=[(0,5,7),(3,-3,-10)]

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  2. If A+2B =[3,1,2),(-4,0,5)],2A-B=[(0,-1,7),(-2,6,1)]find A and B.

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  3. If A=[(2,3),(-1,2)]find A^(4).

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  4. Solve[(x,0,-1)][(1,2,1),(1,1,2),(-2,1,0)][(x,1,0)]=0

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  5. If A=[(2,1,2),(4,2,-3),(0,5,1)],B=[(-2,1,0),(2,1,-1),(1,0,1)].Prove th...

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  6. Express [(3,2,-4),(4,2,-3),(0,5,1)]as sum of symmetric and skew symmet...

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  7. If a(ij)=(2i-j)^(2),find A(32).

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  8. If A=[(3,1,2),(1,2,3)],B=[(1,0),(2,1),(1,1)]find AB and BA.

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  9. If A=[(1,2,3),(4,1,-1),(2,4,6)],find det (A^(T))

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  10. If [(3,-2),(1,2)][(x),(y)]=[(4),(0)],find x and y.

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  11. If A=((2,3),(-1,2)).Show that A^(2)-4A+7I=0whwre I is the unit matrix ...

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  12. If A=[(3,4),(4,-3)]find x if det|A-xI|=0,where I is a unit matrix of o...

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  13. If A=[(2,-1),(1,1)],B=[(1,0),(2,-2)],C=[(3,1),(-1,2)]Show that (i)(A+B...

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  14. Given |(a,a^(2),a^(3)+1),(b,b^(2).b^(3)+1),(c,c^(2)+c^(3)+1)|=0 and a ...

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  15. Solve |(x-1,0,0),(2x,x+3,0),(5x-1,3x+1,x-2)|=0

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  16. If A=|(3,2,-1),(1,0,2),(-2,1,2)|Prove that (i)a(11)A(11)+a(12)A(12)+a...

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  17. If A=|(3,2,1),(1,4,0),(-1,1,2)|and B=|(1,0,1),(1,1,0),(0,0,1)|.Prove t...

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  18. If A=|(cos x,-sin x,0),(sinx,cosx,0),(0,0,1)|.Find A^(n)(by mathematic...

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