MatLAB Answers

A= C=
1 2 3 4 16 2 3 13
6 8 1 5 5 11 10 8
9 4 2 7 9 7 6 12
9 4 7 2 4 14 15 1

B= F=
1 1 1 1 3 6 9 12
1 1 1 1 18 24 3 15
1 1 1 1 27 12 6 21
1 1 1 1 27 12 21 6

Expression:

ABC /4F

Write the Matlab expression and result.

A= C= E=
1 2 3 4 16 2 3 13 1 0 0 0
6 8 1 5 5 11 10 8 0 1 0 0
9 4 2 7 9 7 6 12 0 0 0 1
9 4 7 2 4 14 15 1 1 0 0 0

B= D= F=
1 1 1 1 1 0 0 0 3 6 9 12
1 1 1 1 0 3 0 0 18 24 3 15
1 1 1 1 0 0 5 0 27 12 6 21
1 1 1 1 0 0 0 7 27 12 21 6

Create this matrix from the given matrices (Use matrix shortcuts)

T=
1 2 3 4 2 2 2 2 4 3 3 3
6 8 1 5 2 2 2 2 3 4 3 3
9 4 2 7 2 2 2 2 3 3 3 4
9 4 7 2 2 2 2 2 4 3 3 3
1 4 7 10 16 2 3 13 1 0 0 0
16 22 1 13 5 11 10 8 0 3 0 0
25 10 4 19 9 7 6 12 0 0 5 0
25 10 19 4 4 14 15 1 0 0 0 7

Write Matlab expression and Result

Write the Matlab expression and the result.

A= F=
1 2 3 4 3 6 9 12
6 8 1 5 18 24 3 15
9 4 2 7 27 12 6 21
9 4 7 2 27 12 21 6

Expression
1. 3A+4F

Matlab expression= ???
Result= ?????

plot a sine wave and a cosine wave over one period Make a time vector t from 0 to 2p with enough samples to get smooth lines

Determine of the following Matrix
[1 1 2; 1 3 2; 1 3 4]

Scalar variables. Make the following variables
a. a =10
b. b = 2.5´1023
c. c = +2 3i , where i is the square root of -1
j2 / p 3 d. = , where j is the square root of -1 and e is Euler’s number1 d e (use exp, pi)

1. Throwing a ball. Below are all the steps you need to follow, but you should also add your own meaningful comments to the code as you write it.
a. Start a new file in the MATLAB Editor and save it as throwBall.m
b. At the top of the file, define some constants (you can pick your own variable names)
i. Initial height of ball at release = 1.5 m ii. Gravitational acceleration = 9.8 m/s2
iii. Velocity of ball at release = 4 m/s
iv. Angle of the velocity vector at time of release = 45 degrees

Consider the function f(x) = e
x where e = 2.718 . . . is the base of the natural logarithm
(ln = loge
), sometimes known as Napier’s constant. For x close to 0, e
x
can be approximated by a
finite Taylor series:
e
x ≈ s = 1 + x +
x
2
2! +
x
3
3! +
x
4
4! + · · · +
x
p
p!
where p is a positive integer.
(a) Write a MATLAB program with a for loop to compute (and display) the approximation s of
e
x and the difference d = s − e
x
for p = 1, 2, . . . , num where x and num are entered by the user.
Your program should use format long e and display the values s and d in two columns
with appropriate headings. (Recall that e
x
can be computed in MATLAB using exp(x).)
(b) Run your program with x = 0.5 and num = 10.
(c) Use your program to find the smallest value of p for which the difference s − e
0.5 is less than
10−14 in absolute value.

Consider the parabola defined by y = x
2 − 2x − 1. The distance d(x) from the origin
(0, 0) to a point (x, y) on the parabola is given by
d(x) = q
x
2 + (x
2 − 2x − 1)
2
.
(a) Write a MATLAB program and function M-file to plot d(x) for −2 ≤ x ≤ 4. Also use the
function M-file and the fminbnd command to find (and display) the point (xmin,ymin) on
the parabola that is closest to the origin and display the minimum distance (i.e., the distance
from the origin to the point (xmin,ymin)).
(b) Write a MATLAB program using the fzero command to find the point(s) on the parabola at
distance 4 from the origin.

Write a MATLAB function (not a script!) to generate a periodic waveform of total length
L. Each period must be a pulse of amplitude A that lasts a total of M samples followed by
T − M samples that are zero so that the overall period is T. The result should be a square
wave. You can learn some tricks from the triangular waveform function example in MATLAB
for DSP to write this function without loops. (This is not necessary for full credit.) Note
that this function is not exactly the same in terms of arguments or units. Include a listing
of your function. The function may not call a signal-generating function in the MATLAB
Signal Processing Toolbox.