ESC 251 HW 3 Due: Sep. 12

For this assignment, you should hand in both a written part and a printed part. For the printed part, you should copy and paste your MATLAB commands and output into a Word (or similar) document. Set the document font to Courier New. Remove any extraneous/erroneous commands and augment your MATLAB output to clearly indicate where one problem begins and the next one begins.

1)
(2 pts) Define the following variables:

Perform the following computations in MATLAB and verify the results by hand.
a)
a^2
b)
a*b
d)
a < b
e)
a == b
2)
(1 pt) For a and b as defined in Problem 1), answer the following
a)
What is +a'+?
b)
What is +conj(a)+?
c)
Explain why a) and b) are the same.
d)
Are +a+ and +b+ complex conjugates? Why or why not?
3)
(2 pts) Give the command that will create a row vector from -1 to 1 in steps of 0.1 and store it in the variable x. What are the dimensions of x (hint: use the +size+ command)? Give the output from the following commands and explain the results. If you encounter an error, explain why the error occurs.
a)
+x(2)+
b)
+x(1:11)+
c)
+x(0:22)+
d)
+x(1:2:21)+
e)
+x(21:-1:10)+
f)
+x(1:.1:2)+
Is the last command safe to use?
4)
(4 pts) Create the matrix

Give the output of each command and explain the results. If you encounter an error, explain why the error occurs.
a)
+A(3,1)+
b)
+A(2,3)+
d)
+A(1,0)+
e)
+A(:,2)+
f)
+A(:,1:2:3)+
g)
+A(1,:)+
h)
+A(1:2,2:3)+
i)
+A'+
Define +ii = [3 1]+ and +jj = [3 2]+. Explain the output of
j)
+A(:,jj)+
k)
+A(ii,:)+
l)
+A(ii,jj)+
5)
(2 pts) Give the commands that will create the following quantities:

Now give the command that will use D, e and f to build the matrix A from Problem 4).
6)
(6 pts) Create the following vectors in MATLAB:

Can the following operations be performed? If yes, give the result and verify by hand computation. If not, completely explain why not.
a)
+x * w+
b)
+w * w+
c)
+w' * w+
d)
+y' * z+
e)
+y * z+
f)
+y * y'+
g)
+y .* w+
h)
+y .* w'+
i)
+x .* z+
j)
+x ./ y+
7)
(8 pts) Create the following quantities in MATLAB:

Can the following operations be performed? If yes, give the result and verify by hand computation. If not, completely explain why not.
a)
+A * x+
b)
+x * A+
c)
+A * y+
d)
+y * A+
e)
+A' * x+
f)
+A * y'+
g)
+y' * A * x+
8)
(6 pts) Create the following matrices in MATLAB:

Can the following operations be performed? If yes, give the result and verify by hand computation. If not, completely explain why not.
a)
+A * B+
b)
+A * C+
c)
+C * A+
9)
(2 pts) Let y be defined as in Problem 6). Perform the following calculations and verify the results by hand:
a)
+z = y.^3+
b)
+z = sqrt(y.*y)+
10)
(4 pts) Let D be defined as in Problem 5). Perform the following calculations and verify by hand.
a)
+C1 = D^2+
b)
+C2 = D.^2+
Clearly explain the difference in these 2 calculations.
11)
(2 pts) EXTRA CREDIT: You know that If you have MATLAB compute this, you get the following result:
>> (-1)^(1/3)
ans =
0.5000 + 0.8660i
This is correct, but probably not what you expected. Explain how MATLAB obtained this result.