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Consider the matrix A(alpha)=[(cosalpha,...

Consider the matrix `A_(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)]`
Find all possible real values of `alpha` satisfying the condition `A_(alpha)+A_(alpha)" "^(T)=I.`

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The correct Answer is:
`:. Alpha=2n pi +pi/3`
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PREMIERS PUBLISHERS-MATRICES AND DETERMINANTS-SOLUTION TO EXERCISE 7.1
  1. If A = [(1,a),(0,1)], then compute A^(4).

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  2. Consider the matrix A(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)...

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  3. Consider the matrix A(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)...

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  4. If A = [(4,2),(-1,x)] and such that (A-2I) (A-3I) = 0, find the value ...

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  5. If A = [(1,0,0),(0,1,0),(a,b,-1)], show that A^(2) is a unit matrix.

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  6. If A = [(1,0,2),(0,2,1),(2,0,3)] "and" " "A^(3)-6A^(2)+7A+kI=0,find th...

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  7. Given your own examples of matrices satisfying the conditions in each ...

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  8. Given your own examples of matrices satisfying the conditions in each ...

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  9. Given your own examples of matrices satisfying the conditions in each ...

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  10. Show that f (x) f (y) = f(x+y) , where f(x)=[(cosx,-sinx,0),(sinx,co...

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  11. If A is a square matrix such that A^(2) = A, find the value of 7A-(I+A...

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  12. Verify the property A(B+C) = AB+AC, when the matrices A,B, and C are g...

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  13. Find the matrix A which satisfies the matrix relation A [(1,2,3),(4,5,...

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  14. If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)], verify the ...

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  15. If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)], verify the ...

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  16. If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)], verify the ...

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  17. If A is a 3xx4 matrix and B is a matrix such that both A^(T)B and BA^(...

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  18. Express the matrices as the sum of a symmetric matrix and a skew -sym...

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  19. Express the matrices as the sum of a symmetric matrix and a skew -symm...

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  20. Find the matrix A such that [(2,-1),(1,0),(-3,4)]A=[(-1,-8,10),(1,2,-5...

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