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Control System Homework 1

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Control System Homework 1
1. Basic Arithmetic
Please calculate the following equation and store to variable z1
z1 =
1
2
ln (? + √1 + ?
2) + ?
x = [
2 1 + 2?
−0.45 5

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Control System Homework 1
1. Basic Arithmetic
Please calculate the following equation and store to variable z1
z1 =
1
2
ln (? + √1 + ?
2) + ?
x = [
2 1 + 2?
−0.45 5
]
I : identity matrix.
2. Matrix/Vector
We know that
A = [
12 34 −4
34 7 87
3 65 7
]
B = [
1 4 7
2 5 8
3 6 9
]
Find
(a) z2 = A*B,
(b) z3 = A.*B
(c) z4 = A^3,
(d) z5 = A.^3
(e) z6 = [A([1,3],:);B^2]
(f) z7 = a vector contains eigenvalues of B
(g) z8 = determinant of A
3. Equation Solving
[
1/2 1/3 1/4
1/3 1/4 1/5
1/4 1/5 1/6
][
?1
?2
?3
] = [
0.95
0.67
0.52
]
Solve x1, x2, x3. Then change 0.52 to 0.53 and solve again.
4. Loop statement
Please create a 9*9 Hilbert matrix
Reference: https://en.wikipedia.org/wiki/Hilbert_matrix
5. Plot
Please plot the following equation in one figure, with eq1 on the left and eq2 on
the right.
Eq1:
?1 = − √cos(?) + 3, ??[−
?
2
,
?
2
]
Eq2:
f(x, y) =
?
2
2
2 −
?
2
4
2
, (−2 ≤ ? ≤ 2, −4 ≤ ? ≤ 4)