Question

Math 407 Hosework Two Show step to get full eredit. Name 1, Solve the near system and write your anwr in parsmetrie o S-7ay a-2r+6ry-0 a) 4ay-9ra2ra0 3ry-6ry0 Determine if , and are and 2. Let inly 3. independent. If possible, find a linear dependence relation among these throe vectors. ,m 3. Show that if , are dependent. How about h, m-1? linearly dependent then , must be linearly 4. Show that a linear system AX-0 has a unique solution if and only if the column vectors of A are linearly independent.

I need help with #2

Answer 1

def Given: - vectors vados de are Let scadors a, a, and ag are the a, u tautat az F z = 0 I or I 1 2 50 4 3 solo [5 – 3lol R de, & are the rows :) R₂ 5R, -R3 2 5 1 1 4 3 10 0 11 22 i I x R3 R3 Ti 2 5 I 4 s 10 0 1 2 Too

2-4R, R₂ T2 5 : -5 -10 iv) - 1 3 2 7 R2 1 2 5 102 Io I 2 o & Re - R3 R3 50 - or in O wi) R - R2 R Looo! wil) R, - R2 R, ſolo 10 20 Lo o olo. a, +az = 0 - 0 a + 2a=0 Az =k a= uk a. =-2k

(-k, 2k, k) non trivial solichdes.. It is linearly dependent Relation among these three vectons & a, tag=0 a + 2a=0 a, u + aztet az z = 0 Eaght; +2 a uz & ag 3 = 0 az (-5, - 252 +53) = o as (-(5, + 252) + 3) = 5 = +252 |
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