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. Create a vector of the odd whole
numbers between 31 and 75.

2. Let x = [2 6 1 4 9 3 7 2 8 5].

a.
Add 12 to each element

b. Insert one element in the end of x and set the value to 5.

c. Add 3 to the odd-index elements only.

d. Compute the square of each element.

e. Compute the square root of each element.

f. Delete the odd-index elements of x

3. Let x = [3 1 7 8]' and y = [4 2 3 5]'
(NB. x and y should be column vectors).

a. Sum up the vectors of x and y.

b. Divide each element of x by the corresponding element in y

c. Raise each element of x to the power specified by the corresponding

element in y.

d. Multiply each element in x by the corresponding element in y, name the result
"z".

e. Add up the elements in z

f. Compute x'*y - z.

4. Evaluate the following MATLAB
expressions by hand and use MATLAB to check the answers

a. 2 / 2 * 3

b. 6 - 2 / 5 + 7 ^ 2 - 1

c. 10 / 2 \ 5 - 3 + 2 * 4

d. 3 ^ 2 / 5

e. 3 ^ 2 ^ 2

5. Given the vector x = -1:0.1:1,
explain the results of the following commands:

a. round(x)

b. floor(x)

c. ceil(x)

d. fix(x)

6. Create a vector x with the elements ...

a. 2, 4, 6, 8, 10, 12, 14, ..., 30

b. 10, 8, 6, 4, 2, 0, -2, -4, ..., -20

c. 1, 1/2, 1/3, 1/4, 1/5, ..., 1/20

d. 0, 1/2, 2/3, 3/4, 4/5, ..., 19/20

e. 1, 3, 5, 7, 9, ..., 25, 27, 29, 31, 29, 31, 29, 27, 25, ...,
9, 7, 5, 3, 1

7. Create a vector x with the elements,

x_{n} = (-1)^{n+3}/(2n-1)

Add up the elements of the version of this vector that has 200 elements.

8. Let t = 1:0.2:3,
write down the MATLAB expressions that will correctly compute the following:

a. ln(2 + t + t^{2})

b. e^{t}(1 + cos(3t))

c. cos^{2}(t) + sin^{2}(t)

d. cot(t)

e. sec^{2}(t) + cot(t) - 1

f. tan^{-1}(t)
(this is the *inverse* tangent function)