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If A=[(cos^2alpha,cosalphasinalpha),(cos...

If `A=[(cos^2alpha,cosalphasinalpha),(cosalphasinalpha,sin^2alpha)]` and `B=[(cos^2beta,cosbetasinbeta),(cosbetasinbeta,sin^2beta)]`. Show that `AB=[(cosalphacosbetacos(alpha-beta),sinbetacosalphacos(alpha-beta)),(cosbetasinalphacos(alpha-beta),sinbetasinalphacos(alpha-beta))]`

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BODY BOOKS PUBLICATION-MATRICES-EXERCISE
  1. A=[[1,2,2],[2,1,2],[2,2,1]] , then Find 4A and A^2

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  2. A=[[1,2,2],[2,1,2],[2,2,1]] , then show that A^2-4A=5I3

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  3. If A=[(cos^2alpha,cosalphasinalpha),(cosalphasinalpha,sin^2alpha)] and...

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  4. Let A=[(0,a),(b,0)] Find A^2

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  5. Let A=[(0,a),(b,0)] If A^4=I2 then show that ab=1.

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  6. Of the matrices A=[(2,1,3),(4,1,0)] and B=[(1,-1),(0,2),(5,0)] Find AB...

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  7. Let A=[[2,1,3],[4,1,0]] and B=[[1,-1],[0,2],[5,0]] Show that (AB)^T=...

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  8. If a matrix has 5 elements, write all possible order it can have.

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  9. Consider the matrix A=[(3,10),(2,7)] Express the matrix as A=IA.

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  10. Consider the matrix A=[(3,10),(2,7)] Find A^-1 using elementary row tr...

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

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  12. If A=[(costheta,sintheta),(-sintheta,costheta)] Find A^2

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  13. If A=[[cos theta, sin theta],[ -sin theta, cos theta]], then prove ...

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  14. F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show ...

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  15. F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show ...

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  16. F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show ...

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  17. Write two non-zero matrices A and B for which AB=0.

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  18. Express A=[(1,-1),(2,3)] as the sum of a symmetric matrix and a skew s...

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  19. Let A=[a(ij)](2times3) where a(ij=i+j. construct A.

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  20. For any square matrix A,prove that A+A' is symmetric.

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