MATH 415 Study Guide - Final Guide: Linear Combination, Row Echelon Form, Free Variables And Bound Variables

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

Document Summary

Ax = b cannot have only one solution. 1 there are free variables, thus the system makes the system inconsistent. Since the number of pivots is strictly less than 4, a is noninvertible. Since a is upper triangular a = ia is a valid lu decomposition. What is the number of pivot positions of this matrix? (a) 3 (b) 1 (c) 0 (d) none of the other answers. (e) 2. Let a = (cid:2)a1 a2(cid:3) be a 3 2 matrix and suppose that and ay = . Then the following holds: (a) none of the other answers. (b) (c) (d) (e) (cid:20)1. 1(cid:21) = a1 + 0a2 + 3a3, (cid:20)1. Matrix multiplication is linear combination, so ax = x1a1 + x2a2 for a 3 2 matrix. Consider the following multiplication of two 3 3-matrices, where the question marks represent unknown coe cients: 5 5 c11 c21 c31 c12 c22 c32 c13 c23 c33.