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If P(x)=[cosxsinx-sinxcosx] , then show ...

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

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
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  2. If A=[(3,-5),(-4, 2)] , then find A^2-5A-14 I . .

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

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

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

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

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

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

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

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

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  12. If A=d i ag\ (a\ \ b\ \ c) , show that A^n=d i ag\ (a^n\ \ b^n\ \ c^n)...

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  13. If A is a square matrix, using mathematical induction prove that (A...

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  14. A matrix X has a+b rows and a+2 columns while the matrix Y has b+1 ...

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  15. Give examples of matrices A and B such that A B!=B A . (ii) A and B...

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  16. Give examples of matrices A and B such that A B=O but B A!=O . (ii)...

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  17. Let A and B be square matrices of the same order. Does (A+B)^2=A^2+...

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  18. If A and B are square matrices of the same order, explain, why in g...

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  19. Let A and B be square matrices of the order 3xx3 . Is (A B)^2=A^2B^...

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  20. If A and B are square matrices of the same order such that A B=B A ...

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