Linear systems are particularly easy to solve when theyare in triangular form (i.e., all entries above or belowthe diagonal are zero). a. Solve the lower triangular system | x 1 = − 3 − 3 x 1 + x 2 = 14 x 1 + 2 x 2 + x 3 = 9 − x 1 + 8 x 2 − 5 x 3 + x 4 = 33 | by forward substitution, finding x 1 first, then x 2 ,then x 3 , and finally x 4 . b. Solve the upper triangular system | x 1 + 2 x 2 − x 3 + 4 x 4 = − 3 x 2 + 3 x 3 + 7 x 4 = 5 x 3 + 2 x 4 = 2 x 4 = 0 |
Linear systems are particularly easy to solve when theyare in triangular form (i.e., all entries above or belowthe diagonal are zero). a. Solve the lower triangular system | x 1 = − 3 − 3 x 1 + x 2 = 14 x 1 + 2 x 2 + x 3 = 9 − x 1 + 8 x 2 − 5 x 3 + x 4 = 33 | by forward substitution, finding x 1 first, then x 2 ,then x 3 , and finally x 4 . b. Solve the upper triangular system | x 1 + 2 x 2 − x 3 + 4 x 4 = − 3 x 2 + 3 x 3 + 7 x 4 = 5 x 3 + 2 x 4 = 2 x 4 = 0 |
Solution Summary: The author explains how to find the solution of the linear equation using elimination method.
Linear systems are particularly easy to solve when theyare in triangular form (i.e., all entries above or belowthe diagonal are zero). a. Solve the lower triangular system
|
x
1
=
−
3
−
3
x
1
+
x
2
=
14
x
1
+
2
x
2
+
x
3
=
9
−
x
1
+
8
x
2
−
5
x
3
+
x
4
=
33
|
by forward substitution, finding
x
1
first, then
x
2
,then
x
3
, and finally
x
4
. b. Solve the upper triangular system
|
x
1
+
2
x
2
−
x
3
+
4
x
4
=
−
3
x
2
+
3
x
3
+
7
x
4
=
5
x
3
+
2
x
4
=
2
x
4
=
0
|
eric
pez
Xte
in
z=
Therefore, we have
(x, y, z)=(3.0000,
83.6.1 Exercise
Gauss-Seidel iteration with
Start with (x, y, z) = (0, 0, 0). Use the convergent Jacobi i
Tol=10 to solve the following systems:
1.
5x-y+z = 10
2x-8y-z=11
-x+y+4z=3
iteration (x
Assi 2
Assi 3.
4.
x-5y-z=-8
4x-y- z=13
2x - y-6z=-2
4x y + z = 7
4x-8y + z = -21
-2x+ y +5z = 15
4x + y - z=13
2x - y-6z=-2
x-5y- z=-8
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f
Use Pascal's triangle to expand the binomial
(6m+2)^2
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A falling object travels a distance given by the formula d = 6t + 9t2 where d is in feet
and t is the time in seconds. How many seconds will it take for the object to travel
112 feet? Round answer to 2 decimal places. (Write the number, not the units).
Your Answer:
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