MATH 415 Study Guide - Final Guide: Diagonal Matrix, Oak Ridge National Laboratory, Solution Set

• School: University of Illinois
• Department: Mathematics
• Course: MATH 415
• Professor: J Li

Document Summary

Suppose a is a 3 6 matrix. 0 (b) there is not enough information to determine the answer. (c) no vectors, since dim nul(at ) = 0. (d) (e) . By the ftla, nul(at ) is the orthogonal complement of col(a), thus nul(at ) is one dimensional and spanned by the vector x1 = x3 and x2 = 2x3. Since the orthogonality conditions give the equations. Let a be a 2 2 matrix with eigenvalues 1 and 1 and let i be the 2 2 identity matrix. Which ones of the following are the eigenvalues for the matrix 2a 3i? (a) 2 and 3 (b) 1 and 5 (c) 1 and 0 (d) it cannot be answered with the given information. If is an eigenvalue of a, then 2 3 is an eigenvalue of 2a 3i. Let u and v be two linearly independent vectors in r2. We will check that x and u are linearly independent.