Assignment 3 Vectors and Matrices

Assignment 3
Vectors and Matrices
Task 1 (6 points) Generate the following column vectors using
a) the colon operator
b) the linspace function.
[Note: Your submission should contain two expressions to generate each column
vector, one using a) and another using b) ]
colvec1 = -18
-17
-16
-15
-14
-13
-12
colvec2 = 8
12
16
colvec3 = 16
10
4
Task 2 (9 points) Find an efficient way to generate the following matrix (do not
hardcode the values) (6 points):
M =
10 12 8
13 9 4
21 16 1
29 3 2
Then, give expressions that will, for the matrix M,
A. Write the contents of the element in the last row, third column to variable m1
(1 points)
B. Write the contents of the entire third column to vector m2 (1 points)
C. Write the contents of the second and third rows to matrix M3 (1 points)
Task 3 (20 points) Consider the following vector vec:
vec = [-11 5 3 2 -18 4 -5 5 -66]
The vector vec erroneously stores negative values. We would like to eliminate those
negative values so that we are left with the following values for vec:
vec = [5 3 2 4 5]
Your task is to determine where the negative values are and then to delete them
from the elements of vec. You must present two methods to achieve the task:
a) using the built-in Matlab function find and create new vector called vec1,
b) using a logical vector and create new vector called vec2.
Task 4 (15 points) Write a function that returns the transpose of a given 3x3
matrix without using any of the built in functions (e.g. transpose(M) or rot90(M),
or the transpose operator ‘ ) anywhere in your function. Call this function
transposemat, it will receive on input argument x, which is a 3x3 matrix , and will
return one output argument Y, which is a 3x3 matrix. Example:
x = [1 2 3; 1 2 1; 3 5 1];
y = transposemat( x );
transposemat([1 2 3; 1 2 1; 3 5 1])
ans =
3 by
1 1 3
2 2 5
3 1 1
disp(transposemat([1 2 3; 1 2 1; 3 5 1]))
1 1 3
2 2 5
3 1 1
help transposemat
transposemat(x) returns the transpose of matrix x
Note: The syntax for your function would be transposemat([your_matrix])
Task 5 (25 points) Easter Sunday is the first Sunday after the first full moon of
spring. To compute the date, you can use this algorithm, invented by the
mathematician Carl Friedrich Gauss in 1800:
1. Let y be the year (such as 1800 or 2001).
2. Divide y by 19 and call the remainder a. Ignore the quotient.
3. Divide y by 100 to get a quotient b and a remainder c.
4. Divide b by 4 to get a quotient d and a remainder e.
5. Divide 8 * b + 13 by 25 to get a quotient g. Ignore the remainder.
6. Divide 19 * a + b - d - g + 15 by 30 to get a remainder h. Ignore the quotient.
7. Divide c by 4 to get a quotient j and a remainder k.
8. Divide a + 11 * h by 319 to get a quotient m. Ignore the remainder.
9. Divide 2 * e + 2 * j - k - h + m + 32 by 7 to get a remainder r. Ignore the
quotient.
10. Divide h - m + r + 90 by 25 to get a quotient n. Ignore the remainder.
11. Divide h - m + r + n + 19 by 32 to get a remainder p. Ignore the quotient.
Then Easter falls on day p of month n.
For example, if the value of y is 2001, then: a = 6, b = 20, c = 1, d = 5, e = 0, g = 6,
h = 18, j = 0, k = 1, m = 0, r = 6, n = 4, and p = 15.
Therefore, in 2001, Easter Sunday fell on April 15.
Write a script easterSunday.m (without using any MATLAB toolboxes) that prompts
the user for a year and prints out the year, month, and day of Easter Sunday. Here’s
an example of a possible sample run:
easterSunday
Please enter the year: 2001
In 2001, Easter Sunday fell on 4/15.
throwBall_func.m
Task 6 (25 points) In this week’s lab, you were asked to create a script
throwBall.m. Here, turn the code from a script into a function named
throwBall_func.m. The function takes three arguments v, theta and
maxTime as inputs and returns a logical value (true or false), depending on
whether the ball hits the ground in the allowed time or not. Here is an example of a
function call:
isTrue = throwBall_func(v, theta, maxTime)
While testing the script for Lab 3, you were asking the user to input values for v
and theta. You probably noticed that for certain values of v and theta the ball
did not hit the ground in 20 seconds. Here you are evaluating whether the ball will
hit the ground in maxTime seconds. If none of the values calculated for height (the
vector y) are negative, your call to the function find will return an empty vector.
Use this fact to figure out whether the ball hits the ground in the allowed time or
not. Assign to the return argument variable the appropriate logical value (true or
false).
Note: you must do this WITHOUT using selection statements (IF-ELSE).
Hint: you might want to investigate the function isempty().
Submitting the assignment:
Make sure all your .m files are well commented and they include a comment block
with your name, student ID, course number, assignment number and recitation
section. Zip all the files together and submit the resulting .zip file through Moodle as
Assignment 3 by due date.