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

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: ( Math 205 A B Quiz 03 page 1 09/28/2012 Name. Soagonted Soin 0 2 2 44 2 4 100 -3 0 -1 16 3 9 2 3 010 20 0 Lett A=] -2 3 4 12 3. 8 |;thenrref(AJ=]0 01 00 0 36 0 3 -1 -5 000 01 2 12-1 1-1 -3 000 00 of Let S = {aj, a2, ... , ag} be the set of column vectors of A. 1. Write all solutions of Ax = 0 in parametric vector form: > Ki 3x, + X¢ a \ x= Xy 2 xq + Ox, q © se teal Xz |= Q = Xqy 0 +X, Oo 4 c 4 x4 | O We free ‘ 7 es 4 “2x, O a i ye X¢ Xo | uke de Ob fhe Oond / 2. It’s clear that S is LD. Which vectors in S can be expressed as linear combinations (LC’s) of the other vectors? Don’t write the vectors out; use their names (a, ag, etc.) in a simple list instead. 4» > 2 - > > csr b (OF well Le abe fo fral litms unite OD ta %,8,+%, 9, + 7 +%G6 = O x 9 %> *o) ¥5% Hot need ie & oO; w@ he ape verdes 4 a OR hk, Com be wnltn am Les 4 he ders (be pot Gz-- see 1 below!) 3. If ag can be written as a LC of the other véctors, find a way to do it using as few of the other vectors as possible. Otherwise, explain correctly why a2 is not a LC of the other vectors. the ic 6 0 tal a sok o A= B in chic R vegls Aft &, & MEP O. ty Xy=/ GA X, =O, Thin te ohn Uti One aed ee X22) +0 © 3a + Td, HOR 1ay +0% OH, = BH 20 or, 3B -2ay+B,=8, Sle fe A, td G-t 3a +a, - th nm |B, > me 2 2 (34 ) 3 ial mal& 44 Bay, 4. If ag can be written as a LC of the other vectors, find a way to do it using as few of the other vectors as possible. Otherwise, explain correctly why ag is not a LC of the other vectors. avedor K, Cannt lee vit to 2 LE dhe he ce E. Ra (gre LS of the veel for soppme ik CW B 7 - xa, + x, + Xy4y +X 545 ¢ Xa fr some wn % 9% X, stood Zi, fom bol secs B= KBr +H), the ahh # Xe fp ur av elbing Met (0) that Kat ir AWE al J An 2, ei %& 1 i, BO, gat hina a sob ut y=) a conhrartic bony Gre X; Cat be bth Od -l. So hy BMT GL of hh ahaa.