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

This is the Quiz Solution of Linear Algebra. Mainly include Row Operation, Resulting Matrix, Requirements, Reduced Row Echelon, Reason, Particular Solution etc. Key important points of tags are: Expressed, Parametric Vector, Column Vectors, Solutions, Vectors, Linear Combinations, Explain Correctly, Other Vectors, Written, Way

Typology: Exercises

2012/2013

Uploaded on 02/27/2013

seshu_lin3
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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.