HW5
.docx
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University of Florida *
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Course
3344
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
7
Uploaded by KidArt5006
HW#5
Problem 1. We need to find p
3
given p
0 = [
0
0
1
]
p
1 =
[
0
0
1
]
[
0.95
0
0.05
0.25
0.5
0.25
0.1
0
0.9
]
¿
[
0
∗
0.95
+
0
∗
0.25
+
1
∗
0.1
0
∗
0
+
0
∗
0.5
+
1
∗
0
0
∗
0.05
+
0
∗
0.25
+
1
∗
0.9
]
¿
[
0.1
0
0.9
]
p
2 = [
0.1
0
0.9
]
[
0.95
0
0.05
0.25
0.5
0.25
0.1
0
0.9
]
¿
[
0.1
∗
0.95
+
0
∗
0.25
+
0.9
∗
0.1
0
0.1
∗
0.05
+
0
∗
0.25
+
0.9
∗
0.9
]
¿
[
0.185
0
0.815
]
p
3 = [
0.185
0
0.815
]
[
0.95
0
0.05
0.25
0.5
0.25
0.1
0
0.9
]
¿
[
0.25725
0
0.74275
]
p
3 ¿
[
0.25725
0
0.74275
]
Problem 2
.
[
2
0
1
0
2
0
0
1
0
2
1
0
3
1
0
0
][
29
5
3
8
]
R
3 – 1
2
R
1
[
2
0
0
0
2
0
−
1
1
0
2
1
0
3
1
−
1.50
0
][
29
5
−
11.5
8
]
R
4
R
2
[
2
0
0
0
2
1
−
1
0
0
0
1
2
3
0
−
1.50
1
][
29
8
−
11.5
5
]
R
3
+ R
2
[
2
0
0
0
2
1
0
0
0
0
1
2
3
0
−
1.50
1
][
29
8
−
3.5
5
]
R
4
−
¿
2R
3
[
2
0
0
0
2
1
0
0
0
0
1
0
3
0
−
1.50
4
][
29
8
−
3.5
12
]
Back-substitution {
2
x
1
+
2
x
2
+
3
x
4
=
29
x
2
=
8
x
3
−
1.5
x
4
=−
3.5
4
x
4
=
12
{
x
1
=
29
−
2
∗
8
−
3
∗
3
2
=
2
x
3
=
1.5
∗
3
−
3.5
=
1
x
4
=
3
x
2
=
8
Amount of each compound contained in the sample.
NaMgSi
2
O
6
2
CaFeSi
2
O
6
8
NaMgAl
2
O
6
1
KALSi
3
O
6
3
Problem 3
.
P
=
[
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
]
U
=
[
2
0
0
0
2
1
0
0
0
0
1
0
3
0
−
1.50
4
]
L =
[
1
0
0.5
0
0
1
−
1
0
0
0
1
2
0
0
0
1
]
Problem 4. See gauss_elim.m
Problem 5. See lu_fact.m
Problem 6. See hw5_p6.m
Problem 7. See vector_norm.m
Problem 8. As you can see, the output below shows the norms of Pink, Magenta and Purple when the color code of each is used as a row vector with three values.
Pink, Magenta, Purple 1-norms: 540, 510, 256 2-norms: 329.317, 360.624, 181.019 inf-norms: 255, 255, 128
From the fact that magenta is closer to pink numerically in all three commonly used norms we can conclude that magenta is “closer” to pink.
Problem 9. Here is my “Sun Salutation” sequence, and the video of me performing is attached.
1. Mountain
2. Forward fold
3. Chaturanga
4. Cobra
5. Down Dog
6. Forward Fold
7.Halfway lift
8. Forward Fold
9. Mountain
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