Find the first two iterations of the SOR method with ω
= 1.1 for the
linear...
Find the first two iterations of the SOR method with ω
= 1.1 for the
linear system below using x
(0) = 0.
3x1 − x2 + x3 = 1
3x1 + 6x2 + 2x3 = 0
3x1 + 3x2 + 7x3 = 4
Use Newton's Method to approximate the zero(s) of the function.
Continue the iterations until two successive approximations differ
by less than 0.001. Then find the zero(s) to three decimal places
using a graphing utility and compare the results.
f(x) = x3 − 6.9x2 + 10.79x − 4.851
Newton's method:
Graphing Utility:
x =
x =
(smallest value)
x =
x =
x =
x =
(largest value)
For a first order instrument with a time constant of 0.01 s,
find M(ω) and φ (ω) for the components of the input signal F(t) =
6.5 sin(2π(3.2)t) + 4 sin(2π(32)t). Plot M(ω) and φ (ω) vs. log(ωτ)
on two separate plots. Include M(ω) and φ (ω) points for F(t) on
the appropriate plot. Plot the input and output signals vs. time on
the same graph.
Two 7.1 Ω resistors are connected in parallel, as are two 3.1 Ω
resistors. These two combinations are then connected in series in a
circuit with a 19 V battery. What is the current in each resistor?
What is the voltage across each resistor?
Solve the linear programming problem by the method of
corners.
Find the minimum and maximum of P = 4x +
2y subject to
3x
+
5y
≥
20
3x
+
y
≤
16
−2x
+
y
≤
1
x ≥ 0, y ≥ 0.
The minimum is P =
at (x, y) =
The maximum is P =
at (x, y) =
A lossless 60 Ω line is terminated by a (60 + j60) Ω load.
(a) Find Γ and VSWR.
(b) If Zin = 120 - j60 Ω, how far (in terms of wavelengths) is
the load from the generator?
(c) What fraction of the voltage is reflected?
(d) What fraction of the current is reflected?
(e) What fraction of the power is reflected?
Use the graphical method for linear programming to find the
optimal solution for the following problem.
Maximize P = 4x + 5 y
subject to 2x + 4y ≤ 12
5x + 2y ≤ 10
and x ≥ 0, y ≥
0.
graph the feasible region
Problem 1:
Carry out the first three iterations of the solution of the
following set of equations using the Gauss Seidel iterative
method.Provide the solution using a program, you are free to use
any language including MATLAB.
8x1+2x2+3x3 = 51
2x1+5x2+x3 = 23
-3x1+x2+6x3 = 20
Write two methods. The first method is randFill2DArray. This
method will fill a two-dimensional array with random integers
between a given min and max value. It must accept for parameters,
min and max values for the creation of random integers, and rows
and columns for the number of rows and columns of the array. The
method should return an array of rows by columns size, filled with
random integers between min and max values. The second method is
called printRA,...
Find the best possible relationship using one of the notations:
O, Ω, Θ, o, ω, for the following pairs of functions: n 3 + 6n 1.5 +
3100 and n lg8 − 10n 1.6 − 9000; nlgn and n 1.01; 3n and (3.01)n ;
7n and n!. Justify each answer.
"linear programming". Find out a little more about the history
of how and when this method was developed and in what kinds of
settings it is used. Remember to cite your sources.