Linear Algebra Assignment Solution: Solving Linear Equations Systems

This document presents a detailed solution to a Linear Algebra assignment, specifically addressing the topic of linear systems of equations. The solution demonstrates the application of techniques to solve a system of linear equations by adding and subtracting equations, and scaling equations by a non-zero constant. The assignment involves manipulating equations to eliminate variables and find the values that satisfy the system, which is a fundamental concept in linear algebra. The solution provides a clear, step-by-step approach to solving the given linear systems, making it a valuable resource for students studying linear algebra.

~ ~
~/
1, ,. L('.(,,~J C: ),1l -Aj
L ( (,<_j cj) -- J., c JL - 3 cj
:: C ( '),-"IL - 3j)
~ C L ( )(. 1 ~) • Ii

J'-)
L ( C.)l --; c:3 7 c, t.) ~ ex. t c j 1- c -t-
:: C C1t + ~ t -z_)
:: c,LC)l,~1z.)
1-\: ,\ li'(\ eo-- '<
'

~ ' L ( X \ ~ I 2 J -= )(_ ~ - ·t, ·- j t z

1- . f\ c,(, 1::, J " ct. r '3 ::i ,l - ::1) ✓ ':l " o :\. n. A. •)L == c
)(_, ::: ' l..l, Ct A " tj :: - 1
foy- ~ :: 0 I
A C">l to):: ( x ~')
I I
Fo't' ~::. o,)
A Co, ~ J :: ( 'd :>~ )
1he. ~ -~x.,'.! iJ J~At t~ lle L'.,'\t !1 ~

Qg, ¼cf +:z. -= () . - ' . c0
/ 1
:.(;+ :;__Z- ~ {) ,... (> I)
\ I I
~ - z_ -=- 0 .. p , - (''') p
r. ~,,
r YO >11t, ·~ (_! I l) ) j ~ Z- ,
~ ~dJ b~wrt1 ~ ~ +;z~-=- o ·. .. {{~)
~~v l ~ 5 U1J ~ '1. J. \J•vJ J• ,-,V) 1.J.kh1,-e,.ov. ~ )
~ 1eJ._J_.s {11. t e •H c._ h1t} ),'l-, Q.s .
.". Tr~ o /w.,ti Je,-l:: def,\, -es c., I( >1-e_ qr
0 /J :5 (J .1
1Yl a, f A ; ri--, - ff-c,. J .SNe,,,., ~
A[1,J'J..Jz) -= [,c.+,j+z.J X.,--t-oZ.z.J ';j--z) ~
Jo l \.{_i:/b11.l' 0. re. fbi e... '1.J--e._c...,,b ~ if "°- ~ _x, " z
-=J ..:J J
t~l¼ A (~) --:::: Co) 0.1 o) . I"'- ~.i. <:Ase
__,
rk~ r.I'o' u {(oV\ \
fJ

\
~+J-t-Z ~ d_ • r r •~ )
'"~+ -~z .-::::; 3 ~ r r ( l i)
z_ - ;;i
I
~(I) ,
---:-r:, .x+ ~ :z. -==- 3 . '" -- . (iv) ,
~f ~z:... ~ 2 ~ ,.. r • \ v) ,.
: . lt~ BI ~ t'\ J Q,t def,\, e.J CL !I 11 -Q q ,,-
'f\1 ~ A :1J?3_,. ~ ., !Jfve._Yl, b~
AC½'&J z) -==--- C.)(.t tj-t z ..) x.-t .2. z J 'cf-2 ) ~
J cl ul ibM Cl. re 1"ti e. ~c.. -6n-~ ~ -;::: L~J c'l- J z)-
tN \ ~ A Ca:) -=- 0..J aJ - <><-J . IV\ it, /s - c_a_s e._/

1 -+ er+ z -:;:_ '5
:x_+..:2..-z: '-=:. .1
I
' \!_)
j - z. -=- -1 - - -- ,. , C,·(•·J
F Y-o""'> -€>j_ Ci·;i) _) 8 -=- .1..+ z -
97 :(, +- .z..+.t rt z_ -=- 2 ~
:i_.-t .:2.-z. ~ i . ~ ~ . \2vJ.
~+ ~ z -=- ! _ ~ ,_ ~ . CvJ .
. y I\ L ) p _{_ IL /1' l,'h-e_/",' 'V"'
• ~ I \,\~ j ,\r~V\ dQ_,-C, d __,J,,. ,,\ ~ ~ '--" ,
""0uf A; ~ ➔~ j .9fv'2/t. bcf
A G..) 'ef:/2-) -==- ( ~+i +z J _L-t .2:Z .J }}- z.) __;
,.foIwb'b.,,, a re tti e, w.,c.t,Y.1: ~"" Z ½::1A f
w\+t A l~J =- ( 3 __, i..) 1.) . I'1 14 iJJ
(cue.. J ti; e.,l'Q.. I~ Y\O sol lA°t{b Y) ( e_,y, p"tj)