Prof. Dr. Jörg Wolf
Department of Mathematics, Chung-Ang University
September 13, 2022
1. Exercise Linear Algebra - (due to September 22,2021)
Autumn Semester 2022
1. Solve each of the following linear system by using elementary row operations on the equations or on the augmented matrix.
(a)
x1
+5x2
=7
,
(b)
−2x1 −7x2 = −5
2x1 +4x2 = −4
5x1 +7x2
= 11
2. Consider the following augmented matrices of a linear system that has been reduced by row
operations. In each case continue the appropriate row operations and describe the solution
set of the origional system




1 7 3 −4
1 −2 0 3 −2




0 0 −1 3 
0 1 0 −4 7 




(a) 
(b) 


0 0 0



1
0
0
1
0
6








0 0 1 −2
0 0 0 1 −3
3. Determine if the following linear system is consistent. Do not completely solve the system.
x1
+3x3
=2
−3x4
=3
−2x2 +3x3 +2x4
=1
x2
.
+7x4 = −5
3x1
4. Find an equation involving g, h and k that makes this augmented matrix correspond to a
consistent system.


1 −4 7
g




0
3 −5 h


−2 5 −9 k
5. Consider the following system
x1
cx1
+3x2 = f
dx2
=g
Suppose the system is consistent for all f and g. What can you say about the coefficients
c and d? Justify your answer.