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Using mathematical induction, show that ...

Using mathematical induction, show that
`A^(n)=[(cos n theta,sin n theta),(-sin n theta,cos n theta)]` if `A=[(cos theta,sin theta),(-sin theta,cos theta)], n in N`

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Consider `A^2=[[costheta,sintheta],[-sintheta,costheta]].[[costheta,sintheta],[-sintheta,costheta]]`
`A ^ 2 =[ [ cos ^ 2 θ −sin ^ 2 ...
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NCERT ENGLISH-MATRICES-All Questions
  1. Using mathematical induction, show that A^(n)=[(cos n theta,sin n th...

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  2. If A and B are symmetric matrices of the same order, then show that A...

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  3. Obtain the inverse of the following matrix using elementary operation...

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  4. Find P^(-1), if it exists, given P = [(10, -2),(-5, 1)].

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  5. Express the matrix B=[[2,-2,-4],[-1, 3,4],[ 1,-2,-3]]as the sum of a s...

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  6. By using elementary operations, find the inverse of the matrix A=[[1,...

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  7. If A=[3sqrt(3)2 4 20]and B=[2-1 2 124], verify that(i) (Aprime)prime=A...

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  8. If A=[[-2],[4], [5]], B=[[1 ,3,-6]], verify that (A B)' = B'A'.

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

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  10. The number of all possible matrices of order 3 xx3with each entry 0 or...

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  11. Find x, if [x-5-1][[1, 0 ,2 ],[0,2, 1 ],[2 ,0 ,3]][[x],[4] ,[1]]=O.

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

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  13. Show that the matrix B^TA B is symmetric or skew-symmetric according a...

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  14. If A and B are symmetric matrices, prove that AB – BA is a skew symme...

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  15. For what values of x : [[1, 2, 1]][[1 ,2 ,0],[ 2, 0, 1],[ 1, 0, 2]][[0...

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  16. Find the values of x, y, z if the matrix A=[[0, 2y, z],[ x, y,-z],[ x...

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  17. Let A=[[0, 1],[ 0, 0]]show that (a I+b A)^n=a^n I+n a^(n-1)b A, where...

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  18. If A=[[3,-4],[1,-1]], then prove that A^n=[[1+2n,-4n],[n,1-2n]], where...

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  19. If A=[[1, 1, 1],[ 1, 1, 1],[ 1, 1, 1]], prove that A^n=[[3^(n-1),3^(n-...

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  20. The bookshop of a particular school has 10 dozen chemistry books, 8 d...

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