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If A=[[0,1],[-1,0]], find x\ a n d \ y s...

If `A=[[0,1],[-1,0]],` find `x\ a n d \ y` such that `(x I+y A)^2=A`

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If A=[1-1 2 3],B=[2 1 1 0],p rov et h a t(A+B)^2!=A^2+2A B+B^2

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  2. If A=[1-1 2-1] , B=[a1b-1] and (A+B)^2=A^2+B^2 , then values of a and ...

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  3. If A=[[0,1],[-1,0]], find x\ a n d \ y such that (x I+y A)^2=A

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  4. If A=[alpha0 1 1]a n dB=[1 0 5 1], find the values of alpha for which ...

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  5. Let A-[2-1 3 4], B-[5 2 7 4], C-[2 5 3 8] . Find a matrix D such that ...

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  6. Find the value of x such that [1x1][1 3 2 2 5 1 15 3 2][1 2x]=0

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  7. If A= [[1 , 0],[ − 1, 7]] and I=[[1, 0],[ 0 ,1]] , then find k so that...

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  8. If [2-1 1 0-3 4]A=[-1-8-10 1-2-5 9 22 15],fin dAdot

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  9. Let f(x)=x^2-5x+6 then find f(A) when A=[[2,0,1] , [2,1,3] , [1, -1, 0...

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

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  11. Prove the following by principle of mathematical induction If A=[[3,-4...

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  12. If Aalpha=[[cosalpha ,sinalpha],[-sinalpha,cosalpha]] , then prove tha...

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  13. If Aalpha=[cosalphasinalpha-sinalphacosalpha] , then prove that (Aalph...

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  14. If a is a non-zero real or complex number. Use the principle of mat...

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  15. 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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  16. Under what conditions is the matrix equation A^2-B^2=(A-B)(A+B) is ...

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  17. If A is any mxxn such that A B and B A are both defined show that B...

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  18. A ,\ B are two matrices such that A B and A+B are both defined; sho...

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

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

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