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

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

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If A=[(3,-2) ,(4,-2)] , find k such that A^2-k A-2I^2=O .

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

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

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

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

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

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

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

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

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

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  11. 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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  12. If A=[(1, 2 ,2 ),(2 ,1 ,2),( 2 ,2, 1)] , then prove that A^2-4A-5I=O ...

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  13. If A=[(3, 2, 0),( 1, 4 ,0 ),(0 ,0 ,5)] , show that A^2-7A+10 I=O .

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  14. Without using the concept of inverse of a matrix, find the matrix [...

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  15. Find the matrix A such that : [(1 ,0 ),(0 ,1)]A=[(3 ,3 ,5 ),(1, 0 ,1...

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  16. Find the matrix A such that : [4 1 3]A=[-4 8 4-1 2 1-3 6 3] (iv) [2\ \...

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  17. Find a 2xx2 matrix A such that A[(1,-2),( 1, 4)]=6I2 .

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  18. If A=[[0 ,0], [4 ,0]] , find A^(16) .

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  19. Four uniform spheres, with masses mA=40 kg, mB=35 kg , mC=200 kg , an...

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  20. If A=[(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)] , then verify that A^2+A=A(A+I...

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