Introduction to Programming in MATLAB

1. Working with MATLAB scalars, vectors, and complex numbers.

Using MATLAB, define a unique variable for the following quantities.

a. 5 (ex. Define x = 5, etc.)
b. 25²
c. (3 + 4??) + 8²
d. √(36 + 7²)
e. ??^{(72/5 + 6.54)}
f. the area of a circle of radius 11.21
g. the circumference of the same circle in (f)
h. the area of a square with side length 7.81
i. the side length of a cube of volume 107.81.
j. the magnitude of the vector in (c) (hint: look into real(), imag() or abs())

2. Using built-in functions to manipulate MATLAB variables.

a. define the following vector: (problems a - f)
?? = < √15, 13,34,7², √54, 89.2,0.541,??^7/8, 10, log₁₀ 34.2 >

b. What is the max and minimum value of the above vector? In what elements are these values found?

c. Find the square root, cube root and 7^th root of this vector using a single operation.

d. What is the length of the vector? How many elements does it have? (you must use MATLAB to determine/prove this)

e. Replace the max value of the vector with a value 8.1x its size without redefining the entire vector. Do the same with the minimum value.

f. Create a new, unique, vector containing the 3^rd, 7^th and last values of the vector in (a).

g. Define a vector from 0 to 10 with 100 equally spaced entries (hint: look at linspace)

h. Define a vector ranging from 110 to 120 with a step size of 0.1. What is the length of the resulting vector?

i. Evaluate the trigonometric functions sin and cos from 0 to 2π radians in steps of 0.1.

j. Consider the following vector:

< 1, ??, ??²/2!, ??³/3!, ??⁴/4!, ??⁵/5!, ??⁶/6!, ??7/7!, ??⁸/8!>

define this vector in matlab for a user-selected value of x. Find a MATLAB function that will sum the entries of this vector together. Compare your answer to MATLAB's exp(x) for the same value of x. Are your answers reasonably close?

What does the built-in function you found appear to do?

k. define a random 100 x 1 vector (be sure to suppress the output). What are the mean, median and mode? (hint: use rand(m,n)).

3. Understanding MATLAB matrices.

a. define the following matrices in MATLAB: (problems a - g)

?? = [6, 17, 8]

b. what are the eigenvalues of A (hint: eig())? What is the determinant of A? (find a MATLAB function that can do this for you) What is A^-1?

c. Replace the max and min values of A with the values of a₁₁ and a₁₂, respectively.

d. Create a new matrix from the last two rows of A and the vector B withoutn redefining the system.

e. what is the sum of the first row of A? First column of A?

f. How many elements are in A? B? (must use MATLAB to prove result) Multiply each element in A by 7.2 and each element in B by 2. Find a way to multiply matrices A and B. What must you do? How did you accomplish this?

g. Flip the vector B from right to left. Transpose the matrix into a column vector and flip it once again from up to down.

h. define a random 6x6 matrix, a 3x3 matrix of zeros, 3x3 matrix of ones and the 4x4 identity matrix. (hint: use built-in MATLAB functions). Find a way to combine the random 6x6 matrix, the matrix of ones and the matrix of zeros into a single, 6x9 matrix. (hint: this will likely be a 2 step process).

i. create (another) random 8x8 matrix (be sure to suppress the output). Find a way to define two separate, smaller, 4x4 matrices composed of the values from the "top left" and "bottom right" sub-matrices of the larger, 8x8.

j. Consider the vectors <3,7,1> and <5,2,0>. Find the unit vector of each, a vector normal to both, and the dot product of the two. (hint: look for built-in functions).