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If A=[1 0 2 0 2 1 2 0 3] , then show tha...

If `A=[1 0 2 0 2 1 2 0 3]` , then show that `A` is a root of the polynomial `f(x)=x^3-6x^2+7x+2` .

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If f(x)=x^2-2x , find f(A), where A=[(0, 1, 2),( 4 ,5, 0 ),(0, 2 ,3)...

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

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

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

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

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

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

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

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

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

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  13. If A=[(3,-5),(-4, 2)] , then find A^2-5A-14 I . .

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  14. If P(x)=[cosxsinx-sinxcosx] , then show that P(x)P(y)=P(x+y) .

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  15. If P=[(x,0, 0),( 0,y,0 ),(0, 0,z)] and Q=[(a,0 ,0 ),(0,b,0 ),(0, 0,c)...

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  16. If A=[(2, 0, 1 ),(2, 1, 3),( 1,-1, 0)] , find A^2-5A+4I and hence fi...

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  17. If [[1,1],[0,1]] , prove that A^n=[[1,n],[0,1]] for all positive int...

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  18. If A=[(a, b),(0, 1)] , prove that A^n=[(a^n,b((a^n-1)/(a-1))),(0 ,1)] ...

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  19. If A=[costhetaisinthetaisinthetacostheta] , then prove by principle...

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  20. If A=[cosalpha+sinalpha,sqrt(2)sinalpha; -sqrt(2)sinalpha,cosalpha-sin...

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