MATH 3A Study Guide - Final Guide: Eigenvalues And Eigenvectors, Diagonalizable Matrix, Proj Construction
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MATH 3A Full Course Notes
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There are 5 exercises, worth 100 = 14 + 23 + 23 + 20 + 20 points. Exercise 2 (23= 6 + 2 + 10 + 5 pts) Let a be the following real 4 4 matrix: If yes, nd such a p and d. if no, explain why not. Exercise 3 (23 = 9 + 6 + 3 + 5 pts) Consider the subspace w of r4 given by the equations x1 + x2 x3 = 0 and x1 2x3 2x4 = 0. Exercise 4 (20 = 6 + 3 + 4 + 4 + 3 pts) Let c r be a real number. Consider the real 3 3 matrix ac given by c. Then a2 2a is not invertible. (4) the null space of is 5-dimensional. (5) the real vectors are linearly independent. (cid:20) 0 0. 4 (6) let a be an m n matrix with linearly independent columns.
