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Write the inverse of the matrix: {:[(c...

Write the inverse of the matrix:
`{:[(costheta, -sintheta),(sintheta,costheta)]

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Find the inverse of the matrix : A = [(costheta,sintheta),(-sintheta,costheta)]

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Evaluate the determinant: |[costheta,-sintheta],[sintheta,costheta]|

Find the inverse of each of the folowing matrices: [(cos theta, sin theta),(-sintheta, costheta)]

The value of det [(cos theta, sintheta),(-sintheta, costheta)] is equal to

Prove that AB = BA when: A = {:[(cos theta, sin theta),(sintheta, costheta)] and B = [(cosphi, sin phi),(sinphi, cosphi)]

If A = [(sintheta ,- costheta), (costheta, sintheta)] and B = [(costheta , sin theta),(-sintheta, cos theta)] . Compute (sin theta) A + (cos theta) B.

If A = [[costheta,sintheta],[-sintheta,costheta]] then prove that A^n = [[cosntheta,sinntheta],[-sinntheta,cosntheta]], n in N

Fill in the blanks : If cos 2 theta = 0, then |(0, costheta, sintheta),(costheta, sintheta, 0),(sin theta, 0, costheta)|^2 =……….

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. If A is a square matrix of order 3 swuch that |A|=5, find |A.adj.A|.

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  2. Write the inverse of the matrix: {:[(costheta, sintheta),(-sintheta,...

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  3. Write the inverse of the matrix: {:[(costheta, -sintheta),(sintheta,...

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  4. Verify A(adj A) = (adj A).A = |A|.I :[[2,3],[-4,-6]]

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  5. Verify A(adj A) = (adj A).A = |A|.I : [[1,-1,2],[3,0,-2],[1,0,3]]

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  6. If A = [(costheta,-sintheta,0),(sintheta,costheta,0),(0,0,1)] verify t...

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  7. Find the inverse of each of the following matrices: {:[(-1,5),(-3,2)...

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  8. Find the inverse of each of the following matrices: {:[(2,-2),(4,3)]

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  9. If A = {:[(2,-1),(-1,2)], verify A^2 - 4A + 3I = O, where 1 = {:[(1,0)...

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

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  11. Consider the matrix A = {:[(2,3),(4,5)] Show that A^2-7A-2I=O

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  12. Consider the matrix A = {:[(2,3),(4,5)] Hence , find A^-1

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  13. If A = [ {:(2,3),(5,-2):} ] , write A^(-1) in terms of A.

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  14. Verify that (AB)^(-1) = B^(-1)A^(-1) for the matrices A and B where ...

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  15. Verify (AB)^-1 = B^(-1)A^(-1) for the matrices A and B. Where : A = ...

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  16. Verify that (AB)^(-1) = B^(-1)A^(-1) for the matrices A and B where ...

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  17. Verify (AB)^-1 = B^(-1)A^(-1) for the matrices A and B. Where : A = ...

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  18. Show that the matrix A = [[2,3],[1,2]satisfies the equation A^2-4A+I =...

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  19. If A = [[3,1],[-1,2]], show thatA^2-5A +7I = O

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  20. For the matrix A = [[3,2],[1,1]], find the numbers a and b such that A...

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