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If A=[(1 1 1),( 1 1 1),( 1 1 1)] , then ...

If `A=[(1 1 1),( 1 1 1),( 1 1 1)]` , then prove that `A^n=|(3^(n-1)3^(n-1)3^(n-1)),(3^(n-1)3^(n-1)3^(n-1)),(3^(n-1)3^(n-1)3^(n-1))|` for every positive integer `ndot`

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
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  3. If A=[(1 1 1),( 1 1 1),( 1 1 1)] , then prove that A^n=|(3^(n-1)3^(n-1...

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  7. If A and B are square matrices of order n , then prove that A and B...

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  8. If A B=A and B A=B , then show that A^2=A , B^2=B .

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  9. Give an example of two matrices A and B such that A!=O ,\ \ B!=O ,\ ...

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  10. Give an example of three matrices A ,\ B ,\ C such that A B=A C but...

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  14. Prove that the product of matrices [cos^2thetacosthetasinthetacosthe...

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  15. Let A=[(0,-tan(alpha/2)),(tan(alpha/2),0)] and I be the identity matr...

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  16. Let F(x)=[cosx -sinx 0 sinx cosx 0 ...

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  17. Let A=[2 3-1 2] and f(x)=x^2-4x+7 . Show that f(A)=O . Use this result...

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  18. If A=[0 1 0 0] , prove that (a I+b A)^n=a^n\ I+n a^(n-1)\ b A where I ...

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  19. Let A ,\ B be two matrices such that they commute. Show that for an...

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  20. Let A ,\ B be two matrices such that they commute. Show that for an...

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