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

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
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  2. Give an example of two matrices A and B such that A!=O ,\ \ B!=O ,\ ...

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

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

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

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  10. 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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  11. 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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  12. Let A ,\ B be two matrices such that they commute. Show that for an...

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

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  14. If A is a square matrix such that A^2=A , show that (I+A)^3=7A+I .

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  15. If A is a square matrix such that A^2=I , then find the simplified...

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  16. If A=[3\ \ \ 5] , B=[7\ \ \ 3] , then find a non-zero matrix C such...

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  18. Show that A B!=B A in the following case: A=[5-1 6 7] and B=[2 1 3 ...

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  19. Compute the products A B and B A whichever exists in each of the fol...

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  20. Compute the products A B and B A whichever exists in each of the fol...

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