MT210 QUIZ 4
İLKER S. YÜCE
MARCH 21, 2010
Surname, Name:
QUESTION 1. §1.5 SOLUTION SETS OF LINEAR SYSTEMS
A) Find the solution set of the linear system in the parametric-vector form:
4x1+ 2x2+ 6x3= 2
2x1+x2+ 3x3= 1
6x1+ 3x2+ 9x3= 3
B) Find the solution set of the homogeneous system
4x1+ 2x2+ 6x3= 0
2x1+x2+ 3x3= 0
6x1+ 3x2+ 9x3= 0
ANSWER
A.
4262
2131
6393
−2R2+R1↔R1
−3R2+R3↔R3
//
0000
2131
0000
(1/2)R2↔R1
//
1 1/2 3/2 1/2
0 0 0 0
0 0 0 0
P.V .F . =
1/2
0
0
+x2
−1/2
1
0
+x3
−3/2
0
1
:x2, x3∈R
B.
P.V .F .H . =
x2
−1/2
1
0
+x3
−3/2
0
1
:x2, x3∈R
1