MATH 024 Midterm: math24_2009s_exam3_0
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On the front of your book write (1) your name, (2) a three-problem grad- Show all of your work and box in your nal answers. Unless otherwise mentioned, an answer without the relevant work will receive no credit. 2 : (32 points) (a) de ne (in general) the eigenvalues and eigenvectors of a matrix. (b) find (and justify your answer) the eigenvalues of a = 0 0 3 (c) find the eigenvectors of a . (d) what is the dimension of the subspace spanned by all the eigenvectors of a: (35 points) answer the following true/false questions. 2 = 2x2 2x1} has the same eigenvalues as y 2y + 2y = 0 . (d) the system {x . Then a is invertible and the eigenvalues of a 1 are 1.
