Question

Math 221 Review Linear Algebra II Review 1) In Rº find three distinct non-zero vectors x,y,z which belong to the span of a = -18,-14, 26) B) In dimension of Rº find three distinct non-zero vectors x,y,z, no two of which are parallel to each other, and which belong to the span of a = (17.-5.-15)and b = (21, -3, -17) C) in R solve for a nonzero vector b in the orthogonal complement of a = 190,-17) D) Likewise but for Rºsolve for a nonzero vector b in the orthogonal complement of a = (60,-28,1)

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Answer 1

linear Algebra • To find three distinet non-reso rectors N., 2 which belong to the span of a = (-18, -14, 26) Span (9) -- L & (-18, -14, 26) I & GR}. het & = 2, ²x=29= (-36,- 28,52). at a = 3 = y = 3a = (-54, – 42, 78). at d= –2 = y - a = (+36, 20,-52). © In R² To find a non-zero rector b in the orthogonal complemet of a=(90,-17) en togonal complemetla = (93(1,99 ERC I .9503 = {(1,9 (R? / 903-179=03. Take (2,5) = (1, %:) E(lab)+ InRs To find a non-zes reeks b in the orthogonal. Complement of a = (60,-28, t) tal) & = {(2,9, 2) EH? 1 604-284+2 203 Take ( 28, 10) E (oggt. ③ In 183 To find three non-ren distinctreetess , 32, no two of which are parallel to each other ewlich belach to the span of A= (17,05,15) e b=(2, -3, -17) Spanba, 3) = 24 A + B bl 4, BER} farthers Take x = 29 y=3b. &z= 29+36.