Solutions To Linear Algebra Practice Problems
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18Solutions to Linear Algebra Practice Problems
1. Find all solutions to the following systems of linear equations.
x
2x
+ 2x
=
5
1
2
3
(a)
x
x
=
1
1
2
x
+ x
+ x
=
5
1
2
3
x
+ x
+ 3x
=
3
1
2
3
(b)
x
+ x
+ x
=
1
1
2
3
2x
+ 3x
+ 8x
=
4
1
2
3
Answer:
(a) We create the augmented matrix and row reduce:
1
2
2
5
1
0
0 1
1
1
0
1
0
1
0 2
1
1
1
5
0
0
1 4
Thus, the solutions are x
= 1, x
= 2, x
= 4
1
2
3
(b) We create the augmented matrix and row reduce:
1 1 3
3
1
1
3
3
1 1 1
1
0
1
2
1
2 3 8
4
0
0
0
3
This system is inconsistent. There are no solutions.
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