AE 280 Bethesda University Methods of Analysis Differential Equations HW6 help me with my homework 10 questions attached belowthey are 10 questions about d

AE 280 Bethesda University Methods of Analysis Differential Equations HW6 help me with my homework 10 questions attached belowthey are 10 questions about differential equation and methods of analysis May 27, 2020
AE 280 Summer 2020
Homework Six
Due: Saturday July 4, 2020
Exercise 1 Evaluation of determinants:
A=
cos ? sin ?
sin ? cos ?
B=
cos n? sin n?
? sin n? cos n?
4 ?1 8
C= 0 2 3
0 0 5
Exercise 2 Solve by Cramer’s rule.
a)
2x ? 4y = ?24
5x + 2y = 0
b)
3y ? 4z = 16
2x ? 5y + 7z = ?27
?x ? 9z = 9
c)
3x ? 2y + z = 13
?2x + y + 4z = 11
x + 4y ? 5z = ?31
Exercise 3 Find the inverse
a)

cos 2? sin 2?
? sin 2? cos 2?
b)
?
?
1 0 0
?2 1 0?
5 4 1
c)
?
?
?4 0 0
? 0 8 13?
0 3 5
1

a b c
D= c a b
b c a
d)
?
?
0 1 0
?1 0 0?
0 0 1
e)
?
?
1 2 3
?4 5 6?
7 8 9
f)
?
2
3
?? 2
3
1
3
1
3
2
3
2
3
2
3
1
3
? 23
?
?
Exercise 4 Find the eigenvalues and the corresponding eigenvecters

5 ?2
1 2
1 2
A=
B=
C=
9 ?6
2 4
0 3
Exercise 5 Solve the following initial valaue problems using eigenvalue method.
a)
y10 = 2y1 + 2y2
y20 = 5y1 ? y2
y1 (0) = 0, y2 (0) = 7
b)
y10 = y2
y20 = y1
y1 (0) = 0, y2 (0) = 2
2

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