The following exercises are meant to be answered by a single MATLAB command. The command may be involved (i.e., it may use a number of parentheses or calls to functions) but can, in essence, be solved by the execution of a single command. If the command is too complicated, feel free to break it up over two or more lines.
1. Given the matrix A = [2 9 6 8 ; 3 2 7 5 ; 8 2 3 5], provide the commands needed to
a.
assign the element in the first row and second column of A called y
b. assign the elements of four corners to 2by2 matrix
called y
c. assign the first row of A to a vector called y
d. assign the evennumbered columns of A to an matrix called
y
e. assign the oddnumbered rows of A to an matrix called y
f. assign the last 3 columns of A to an matrix called y
g. transpose A into a 4by3 matrix
h.
change size A into a 4by3 matrix, using the command
"reshape" may be helpful here.
2. Create the 3by3 matrix M with integers number between 0 and 50 (include 0 and 50)
randomly.
3. Given the matrix A = randn(4),
provide the command that will
a.
compute the determinant of A
b. compute the mean of all elements of A
c.
compute the product over the rows of A
d. compute the sum over the columns of A
e. compute
the inverse of A
f. compute the standard error of each column of A (NB. the standard
error is defined as the standard deviation divided by the square root of the
number of elements used to compute the mean.)
4. The mechanical work W done in using a
force F to push a block through a distance D is W = FD. The following table
gives data on the amount of force used to push a block through the given
distance over five segments of a certain path. The force varies because of the
differing friction properties of the surface.
Path 

1 
2 
3 
4 
5 
Force 
(N) 
410 
540 
700 
500 
570 
Distance 
(m) 
2 
0.5 
0.65 
1.5 
3.5 
Use Matlab to
find
a) the work
done on each segment of the path.
b) the total
work done over the entire path.
5. Solve the following for y.
6. Given B, C, and D:
Find A where C(A
+ B) = D.
7. Six people, Fred, Grace, Harry, Irene, Jerry, and Kim, each
have a debit card.
q
The total
money owed on all six credit card balances is $456.
q
Fred owes twice as much money
as Irene.
q
Jerry and Kim's total balances equal Grace's.
q
Irene and Jerry's total balances equal the total of
Grace and Harry's.
q
If you
subtract Grace's balance from Harry's, the total is twice Irene's.
q
The sum of
Jerry and Grace's balances are greater than Harry's by $115.
a. Write the linear set of
equations.
b. Write all of the MATLAB code needed to solve the problem.
c. Who owes money and how much? Who has credit and how much?