Linear Combination - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

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a Math 205B&C Quiz 01 page 1 01/01/09 Name Sug gestedt La Me Section: 8am 1:10 pm 1 -1 2 —5 6 1. Let vi = |-3], v2= | 1 |, v3 = |—7]. Also, let b= | 11] and c= |—10]. 2 0 5 -5 4 1A. In terms of the definition, explain what it means to eR ‘Ss b a linear combination of v,, v2, and v3?" Your answer should start with, “are there scalars a). "Dre there stabs ay Oy Gnol A, 4 heh Gea, +H, v, ace 1B. Now, determine if b actually is a linear combination of v,, v2, and v3. Explain how you decide. wwe Contr. He Correapen ding i , 25] 0 mented mnodcix [ fo -) 2 7 chal. bm peer {5 gels 59 ms t -p “ , 1 [oe Be as As } He Lyslem Corteapon dy b Me PET te # treencilart, 4a Oy, + Ou, + On, = i Cink Le. colved , Theebe. & & Moe a LE Sf G / a wot ie 1C. To determine if ¢ is in the span of {v1, v2, vg} is equivalent to solving what system of linear equations? : x, r ex, = 6 Toe) bh ag . a fe 2x, #S%q, = 1 1D. Find all solutions to the system produced in part (C). the aeepeaty — matrix & |-3 1 3 “0 hal he ener | i eefA Ae sh end cn 2 9 Syskins one eo ee 1E. What specific solution do you get if you set any and all free variables in part (D) to the woth 2" free Verify that your solution works by evaluating the corresponding linear combination of v,, v2, and v3 ih X,=2 we dian SX, os of 0.502, = -4- = -5 So fhaspeifd sch 6 (35-5, 2) Checde: Aes afi-{3) 4) : “345449426 He ae 9-19 = 10 ~6 te Fy