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Unformatted text preview: 1 , ~v 2 = 1 2 3 4 , ~v 3 = 1 31 1 5. (12 pts) (a) Find a 2 Ã— 2 matrix A whose eigenvalues are Î» 1 = 1 2 and Î» 2 = 3 2 with corresponding eigenvectors ~v 1 = " 4 2 # and ~v 2 = " 24 # . (b) Sketch the phaseportrait for the dynamical system ~x ( t + 1) = A~x ( t ). (c) If D is the unit disk and if T ( ~x ) = A~x then what is the area of T ( D )? 6. (9 pts) (a) A 4 Ã— 4 matrix A has eigenvalues1 , 1 , 3 , 5. What is the determinant of A1 ? (b) Given that Î» is an eigenvalue for the 4 Ã— 4 matrix A , use this to Fnd an eigenvalue for the matrix A 2A . (c) If A and B are n Ã— n orthogonal matrices, then show that AB is also an orthogonal matrix....
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 Spring '08
 Staff
 Math, Linear Algebra, Algebra, Matrices, Eigenvalue, eigenvector and eigenspace, Orthogonal matrix, Wednesday 2PM deadline

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