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If A=[[1 , 2 , 3],[ 3, -2 , 1],[ 4, ...

If `A=[[1 , 2 , 3],[ 3, -2 , 1],[ 4, 2 , 1]]`, then show that `A^3-23 A-40 I=0`

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V PUBLICATION-MATRICES-QUESTION BANK
  1. Find A B, if A=[[0, -1],[ 0 , 2]]and B=[[3 , 5],[ 0, 0]]

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  2. A=[[0 , 6 , 7 ],[ -6, 0 , 8 ],[ 7, -8, 0]], B=[[0, 1 ,1],[ 1 , 0...

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  3. If A=[[1 , 2 , 3],[ 3, -2 , 1],[ 4, 2 , 1]], then show that A^3-23...

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  4. Let A=[[2 , 4 ],[ 3, 2]], B=[[1, 3] ,[ -2 , 5]], C=[[-2 , 5 ],[ 3, ...

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  5. Compute the following: i)[[a, b],[ -b, a]]+[[a, b],[ b , a]]. i...

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  6. Compute the indicated products. i) [[a , b],[ -b , a]] [[a, -b],[ b...

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  7. If A =[[1, 2, -3],[ 5, 0, 2],[ 1, -1, 1]], B=[[3, -1, 2],[ ...

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

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  9. Simplify costheta[[costheta, sin theta],[-sintheta, costheta]]+sinthet...

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  10. Find X and Y, if i) X+Y=[[7, 0],[ 2, 5]] and X-Y=[[3 , 0],[ 0 , 3...

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

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  12. Find x and y if 2[[1,3],[0,x]]+[[y,0],[1,2]]=[[5,6],[1,8]]

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  13. Solve the equation for x, y, z and t, if 2[[x, z],[ y, t]]+3[[1, -...

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  14. If x[[2],[3]]+y[[-1],[1]]=[[10],[5]] find the values of x and y.

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  15. Given 3[[x,y],[z,w]]=[[x,6],[-1,2w]]+[[4, x+y],[z+w, 3]] find the va...

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  16. F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show ...

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  17. Show that i) [[5 , (-1)],[ 6, 7]][[2, 1],[ 3 ,4]] ne[[2 , 1 ],[3 ,...

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

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

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

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