MATH 3A Study Guide - Midterm Guide: Linear Map, Row Echelon Form, 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. Exercise 2 (28 = 7 + 15 + 6 pts) Points is 10 + 4 #correct. (1) the vectors [1, 2, 3]t and [2, 4, 5]t are linearly dependent. (2) let t : rn rm be a linear transformation. Then t is one-to-one. (5) let a be an n n matrix and let x rn be such that ax = x for some r. Then one has a42x = 42x. (6) let a be a matrix with n columns, p pivots and f free variables. Then one has n = p + f . (7) let t : r7 r3 be a linear map.
