Fix a value a R. Consider the matrix A = (cos(a)2-sin(a)2 2 cos(a) sin(a) 2 cos(a)...

 

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Fix a value a R. Consider the matrix A = (cos(a)2-sin(a)2 2 cos(a) sin(a) 2 cos(a) sin(a) sin(a) cos(a)2). (a) Determine the eigenvalues A1 and A2 of A. (Hint: For simplicity, you can write c = cos(a) and s=sin(a), and recall that c+s2=1 by Pythagoras's Theorem.) (b) Now set a = . For each eigenvalue A1 and A2 from part (a), determine eigenvectors x1 and x2. (c) Still assume a=. In the diagram below (or a copy of it), draw the lines spanned by x and x2 from part (b), and for the vector v=(2), draw the vectors v and Av. Fix a value a R. Consider the matrix A = (cos(a)2-sin(a)2 2 cos(a) sin(a) 2 cos(a) sin(a) sin(a) cos(a)2). (a) Determine the eigenvalues A1 and A2 of A. (Hint: For simplicity, you can write c = cos(a) and s=sin(a), and recall that c+s2=1 by Pythagoras's Theorem.) (b) Now set a = . For each eigenvalue A1 and A2 from part (a), determine eigenvectors x1 and x2. (c) Still assume a=. In the diagram below (or a copy of it), draw the lines spanned by x and x2 from part (b), and for the vector v=(2), draw the vectors v and Av.