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If A=[[costheta,sintheta],[-sintheta,cos...

If `A=[[costheta,sintheta],[-sintheta,costheta]]`, then prove that `A^n=[[cosntheta,sinntheta],[-sinntheta,cosntheta]], 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-MATRICES-SOLVED EXAMPLES
  1. If A=[[costheta,sintheta],[-sintheta,costheta]], then prove that A^n=[...

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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=[(3,sqrt(3),2),(4,2,0)]and B=[(2,-1,2),(1,2,4)], verify that (i) ...

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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. If A=[[1,-2, 3],[ 4, 2, 5]]and B=[[2, 4],[ 2,3],[ 5, 1]], then find AB...

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  11. Find AB, if A=[[6, 9],[ 2, 3]]and B=[[2 ,6, 0],[ 7, 9, 8]].

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  12. Two farmers Ramkishan and Gurcharan Singh cultivates only three varie...

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  13. Find the values of x and y from the following equation:2[[x,5],[ 7,y-...

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  14. If A=[[0, 6, 7],[-6, 0, 8],[ 7,-8, 0]], B=[[0, 1, 1],[ 1, 0, 2],[ 1, 2...

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  15. If A=[1 1-1 2 0 3 3-1 2], B=[1 0-13 2 4]and C=[1 2 3-4 2 0-2 1], find ...

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  16. Find AB, if A=[[0,-1],[ 0, 2]]and B=[[3, 5],[ 0, 0]].

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  17. If A=[[1,0],[ 0,-1]]and B=[[0, 1],[ 1 ,0]], then A B=[[0,1],[-1, 0]]an...

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  18. In a legislative assembly election, a political group hired a public ...

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  19. If A=[[1,2, 3],[ 3,-2 ,1],[ 4, 2, 1]], then show that A^3-23 A-401=0.

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  20. If A=[[8,0],[4,-2],[3,6]]and B=[[2,-2],[4,2],[-5,1]], then find the ma...

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