01:640:250 Study Guide - Civi-Dt, Diagonalizable Matrix, Linear Independence
30 Oct 2014
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This problem set concentrates on material from the end of the course. For a complete review, you should also study the review problem sets for the two in-class exams. Please consider these earlier problem sets as implicitly included with this one. 2 2 3 (a) find an orthonormal set of eigenvectors of a which form a basis for r3. Show that x and v are orthogonal: state the cauchy-schwarz inequality and the triangle inequality, and show that the former implies the latter, given that u = . A 4 4 matrix a is necessarily diagonalizable if: T f (b) a has four linearly independent eigenvectors; T f (c) the eigenvalues of a are 7, 2, and 0, and a has rank 2; T f (d) the characteristic polynomial of a is ( 2 1)( 2 2): (a) find the eigenvalues and eigenvectors of the matrix a = (cid:20) 4 2.
