Answers Key for Quiz 3 - Introduction Applied Linear Algebra | MATH 254, Quizzes of Linear Algebra

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Math 254-2 - Introduction to Linear Algebra, Fall 2006, Professor: Rakhim Aitbayev September 21, 2006 Quiz 3 Name: Solu tiou Keg. 2 —6 8 1. Find the values of h for which the set of vectors is linearly dependent: | —4 | : | 7 | ; | h | | = 2-6 8 1-3 4 VAei oe =f -4 Th |-s|l-4yqous, ; a -£ tél 173 4 1, -34y °o Oo 0 She veefors are Cimace by dep en dent doe as heR | 2. Find the standard matrix of a linear transformation T : A? — R? that first contracts horizontally by a factc of 0.5 and then reflects points through the line 2 = 2}. (THE fe The motix ot T. ; T)= [Te Tey whe ae (3), e= (4) we)= [° jem (THT Ties fF) sine [2-U\- 154 Thas, [T3= \ in i 1 3 2 = 3. The linear transformation T : R? — R? is such that T(e,) = 9 , Tes) = mt , T(es) = i where e; is the i standard basis vector in R? for i= 1,2,3. Is mapping T onto, one-to-one, or a bijection Explain. \ (T3= [rle), Te) We) = [27 *\ fa T 6 net one-t-one Since " pocEscnt ok 8 Tis hot & gs jechen Sjhe ae wot oie to one eee = [3 @ EAE “There are pol psi Rone vs all ° eS = Tu wo oul,