4. For what values of h and k is the following system consistent?
2x1
x2 D h
6x1 C 3x2 D k
1.1 Exercises
Solve each system in Exercises 1–4 by using elementary row
operations on the equations or on the augmented matrix. Follow
the systematic elimination procedure described in this section.
1. x1 C 5x2 D 7
2x1
2. 2x1 C 4x2 D
7x2 D
5
4
5x1 C 7x2 D 11
3. Find the point .x1; x2/ that lies on the line x1 C 5x2 D 7 and
on the line x1 2x2 D
2. See the !gure.
x1 1 5x2 5 7
x2
x1 2 2x2 5 22
x1
2 13
1150
5. 6
6 00107
4
0001
13
7
3 57
In Exercises 7–10, the augmented matrix of a linear system has
been reduced by row operations to the form shown. In each case,
continue the appropriate row operations and describe the solution
set of the original system.
5x2 D 1 and
Consider each matrix in Exercises 5 and 6 as the augmented matrix
of a linear system. State in words the next two elementary row
operations that should be performed in the process of solving the
system.
8 7
7
5
6
2 1
640
02
704
6. 6
6 0012
4
00316
7.
4. Find the point of intersection of the lines x1
3x1 7x2 D 5.
3
409
9.
2 173
01
6
6 0001
4
001
43
13
2 1
100
30
6 01
6 001
4
00004
2
3
2 1150
8. 4 0 1 9 0
007
7
7
5
3
7
5
43
7 7
1 7
5
Sida 36 av 670
1.1 Systems of Linear Equations 35
10.
2 1
2030
6 010
6 00100
4
00010
3
40
7
7
5
22. Do the three planes x1 C 2x2 C x3 D 4, x2
x3 D 1, and
x1 C 3x2 D 0 have at least one common point of intersection? Explain.