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If A=[(3, 2, 0),( 1, 4 ,0 ),(0 ,0 ,5)] ,...

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

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
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  2. If A=[(1, 2 ,2 ),(2 ,1 ,2),( 2 ,2, 1)] , then prove that A^2-4A-5I=O ...

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

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

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

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

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

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

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

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

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

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

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

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

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  19. If A=[1 1 1 0 1 1 0 0 1] , then use the principle of mathematical in...

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  20. If B ,\ C are n rowed square matrices and if A=B+C , B C=C B , C^2=...

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