Homework #1
1. (a) Write out the results of each step of Gaussian elimination on the augmented
matrix form for the linear equation
2
x

3
y
+
z
= 1
x
+
y

z
= 2

4
x
+ 4
z
=

1
.
(b) Use back substitution to solve for
x
,
y
, and
z
.
(c) Write out the results of each step of Gaussian elimination with row pivoting on
the augmented matrix form for the same linear equation.
2. Solve the following linear system of equations using Gaussian elimination with row
pivoting:
2
x
1
+
x
2
+
x
3

x
4
= 4

4
x
1

2
x
2
+
x
3
+ 2
x
4
=

2
2
x
1
+ 2
x
2

x
3

2
x
4
=

1

x
1
+ 4
x
2

2
x
3
+
x
4
= 0
3. (a) Solve the following linear system of equations using Gaussian elimination with
row pivoting under threedigit rounding:
(
0
.
002
x

4
y
=

2
x
+ 4
y
= 3
(b) Solve the following linear system of equations using Gaussian elimination with
row pivoting under threedigit rounding:
(
2
x

4000
y
=

2000
x
+ 4
y
= 3
(c) Which of the approximations is closer to the exact solution
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 Spring '08
 staff
 Gaussian Elimination, 0.00001 seconds, 0.000015 seconds

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