% Define matrix A one element at a time.
%% Lab 2 – Your Name – MAT 275 Lab
%% Example code
% Example 1
% NOTE: Delete examples before submission.
A = [1 0; 0 -1]
A = [1, 0; 0, -1]
% NOTE: The two matrices above are the same. We can separate columns with
% commas OR spaces, and separate rows with semi-colons.
%%
% The following code changes the element in the 1st row and 2nd column of
% matrix A to 9. In general, we can extract or change elements in a matrix A
% with the syntax A(row,column).
A(1,2) = 9
%%
% We can create the original matrix A above one element at a time as
% follows:
% Initiate A as empty vector (optional but necessary in other cases).
A = [];
% Define matrix A one element at a time.
A(1,1) = 1;
A(1,2) = 0;
A(2,1) = 0;
A(2,2) = -1;
% Display vector A.
A
%%
% This example shows how we can extract elements, rows, or columns from a
% matrix. A colon indicates “all elements.” So A(2,:) extracts elements in
% all columns of A that are also in the 2nd row of A. Note: To run this
% section, a matrix A must be saved in the workspace.
disp(‘Extract second row’) % disp command displays a specified string
A(2,:)
disp(‘Extract first column’)
A(:,1)
disp(‘Extract last element’)
A(end,end)
%%
% Let’s declare a vector b and sove Ax = b where A is a known matrix, b is
% a known vector, and x is an unkown vector with same dimensions as b. This
% is the most fundamental problem in linear algebra.
b = [1;2];
x = A\b % solve Ax = b using backslash command
% NOTE: These examples are not comprehensive. Make sure you also go through
% the protocol examples.
%% Exercise 1
% Part (a)
%%
% Part (b)
%%
% Part (c)
% NOTE: Use the “backslash” command. NOT the division operator “/”.
%%
% Part (d)
%%
% Part (e)
%%
% Part (f)
%% Exercise 2
% Part (a)
% NOTE: We must create separate function M-files here. The function will
% require input variables. Therefore, you cannot use “run” to execute the
% function. You must invoke it by providing values for the input variables.
% Suppose we name our function geom_sum. Then complete the following.
% NOTE: You MUST comment each line of code in you M-file similar to how I
% comment each line of code in this script file. You may choose your own
% style of documentation, but make sure it is consistent throughout the
% semester and thoroughly explains what the code is doing. Further, you
% should have a comment at the beginning of each function file explaining
% what the function does. I WILL MARK OFF POINTS otherwise.
% Display contents of geom_sum M-file.
type ‘geom_sum.m’
% Assign values to input variables.
r = ??;
a = ??;
n = ??;
% NOTE: Do NOT define r,a, or n inside the function file. This defeats the
% purpose of requiring input arguments.
% Compute geometric sum for specified values of r,a, and n.
geom_sum(??)
%%
% Part (b)
% NOTE: MATLAB has several built in functions. Here, we want to use the
% built-in function “sum” to compute the same geometric sum as computed in
% part (a). If x is a vector, then “sum(x)” sums all the elements of x.
% Therefore, the “sum” function takes a vector as input and sums its
% elements. Hence, we must create a vector containing all the terms of the
% sum we wish to compute and pass that vector as input to the sum function.
%% Example for 2b
x = [1, 1, 1];
sum(x)
% NOTE: Answer should be 1 + 1 + 1 = 3. Type “help sum” in command window
% for more info.
%% Exercise 3
% Part (a)
% NOTE: When the protocol says to write a script file, you do not need to
% create a separate M-file. This main file is a script file and you can
% simply write the list of commands here. Please refer to the second
% example on page 5 before attempting this problem.
% Initiate product P.
P = ??;
% Define starting iteration index.
m = ??;
% Define stepsize of iteration.
k = ??;
% Define ending iteration index.
n = ??;
% Compute product.
for i = m:k:n
<code> % muliply P by next element at each iteration (suppress output)
end
% Display product.
<code>
% NOTE: i = m:k:n is also a vector! A for-loop essentially iterates through
% each element of a vector. Keep this in mind for part (b).
% NOTE: Type “help for” in the command window for more info.
%%
% Part (b)
% NOTE: Emphasis on the part where it says “SINGLE COMMAND.” That means ONE
% line of code. The “prod” function is another built-in function that,
% similar to “sum”, takes in a vector as input, yet computes the product of
% all the elements of the input vector. So, we need to create a vector
% containing all the numbers between 1 and 15 with a stepsize of 2. Which
% vector declaration method is best when we know the stepsize? Also, in
% order to compute the product in a single command, we must declare the
% vector INSIDE the prod command as an input argument, as opposed to x =
% vector, prod(x). Instead, we do prod(vector). Type “help prod” in the
% command window for more info.
%% Exercise 4
% NOTE: When the protocol says to write a script file, you do not need to
% create a separate M-file. This main file is a script file and you can
% simply write the list of commands here. Refer to second example on page 6
% of protocol before attempting this exercise.
% Initiate variables.
power = ??;
k = ??; % initiate counter
% Initiate vector V of powers of 3.
V = ??;
% Compute powers of 3 and store in V.
while ?? < ?? % specify condition of while-loop: stop iterating once
% condition is no longer satisfied
power = ??; % compute next value of power at each iteration
V = ??; % concatenate vector V with new element at each iteration
k = ??; % increment counter k
end
% Display vector V.
<code>
%% Exercise 5
% NOTE: Here, we must create a separate function M-file f that accepts one
% input argument, a value of the variable x. You may want to start creating
% a new folder for each lab as we will be using f multiple times to define
% different functions. Please refer to the example on the last page of the
% protocol before attempting this problem.
% Display contents of function f M-file.
type ‘f.m’
% Evaluate f at x = 1.
f(??)
% Evaluate f at x = 2.
<code>
% Evaluate f at x = 3.
<code>
% Evaluate f at x = 4.
<code>
% Evaluate f at x = 7.
<code>
% Evaluate f at x = 10.
<code>
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