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If A=[[3 ,1],[-1 ,2]] and I=[[1, 0],[ 0,...

If `A=[[3 ,1],[-1 ,2]]` and `I=[[1, 0],[ 0, 1]]` , then find `lambda` so that `A^2=5A+lambdaI`

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If [1\ -1\ \ x][[0, 1,-1 ],[2 ,1 ,3],[ 1, 1, 1]][[0 ],[1],[ 1]]=0 , fi...

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  2. If A=[ (3,-2),( 4 ,-2) ] and I=[(1,0),(0,1)] , then prove that A^2-A+2...

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  3. If A=[[3 ,1],[-1 ,2]] and I=[[1, 0],[ 0, 1]] , then find lambda so tha...

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  4. If A=[[3 ,1],[-1, 2]] , show that A^2-5A+7I^2=O .

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  5. If A=[(2, 3),(-1 ,0)] , show that A^2-2A+3I^2=O .

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  6. Show that the matrix A=[(2, 3), (1, 2)] satisfies the equation A^3-4A...

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  7. Show that the matrix A=[(5, 3), (12 ,7)] then show A^2-12 A-I=O .

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  8. If A=[(3,-5),(-4, 2)] , find A^2-5A-14 Idot

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  9. If A=[[3, 1],[-1 ,2]] , show that A^2-5A+7I=O . Use this to find A^4

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  10. If A=[(3,-2) ,(4,-2)] , find k such that A^2-k A-2I^2=O .

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  11. If A=[(1, 0),(-1 ,7)] , find k such that A^2-8A+k I=O .

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  12. If A=[(1 ,2 ),(2, 1)] and f(x)=x^2-2x-3 , show that f(A)=O .

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  13. Find dy/dx if logy=5x^2

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  14. Find the value of x for which the matrix product [(2, 0, 7),( 0, ...

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  15. Solve the matrix equations: [(x,1)][(1, 0),(-2,-3)][(x,5)]=0

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  16. Solve the matrix equations: [2x\ \ 3][(1, 2),(-3, 0)][(x),(8)]=0

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  17. If A=[(1, 2, 0 ),(3,-4, 5),( 0,-1, 3)] , compute A^2-4A+3I .

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  18. If f(x)=x^2-2x , find f(A), where A=[(0, 1, 2),( 4 ,5, 0 ),(0, 2 ,3)...

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  19. If f(x)=x^3+4x^2-x , find f(A) , where A=[(0 ,1, 2 ),(2,-3 ,0),( 1,-...

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  20. If A=[1 0 2 0 2 1 2 0 3] , then show that A is a root of the polyno...

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