MATH 3A Study Guide - Midterm Guide: Row Echelon Form, Linear Map, Augmented Matrix
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MATH 3A Full Course Notes
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There are 3 exercises, worth a total of 100 = 42 + 28 + 30 points. Provide computations and or explanations, unless stated otherwise. Exercise 1 (42 = 6 + 16 + 8 + 5 + 7 pts) If they are dependent, nd a linear dependence relation among the columns of a. For examle, second column minus fourth column is 0 ( nd any vector in null space: you can nd null space from c, which is just x4[0, 1, 0, 1, 0]t + x5[1, 0, 2, 0, 1]t ). Exercise 2 (28 = 7 + 15 + 6 pts) Solution: (a) one can compute the rref of [u1u2u3], which is the identity: this means that any augmented system is consistent. But, in our case, we can use our expressions from (a) to nd: (cid:20) 0. This matrix satis es the required properties, and is unique. (c) in nitely many.
