\documentclass[12pt,a4paper,pdftex]{exam}
\newcommand{\exercisetopic}{Vectors}
\newcommand{\exercisenum}{2}
\newcommand{\exercisedate}{3. November, 2020}
\input{../../exercisesheader}
\firstpagefooter{Dr. Jan Grewe}{}{jan.grewe@uni-tuebingen.de}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\input{../../exercisestitle}
The exercises are meant for self-monitoring and revision of the lecture
topic. You should try to solve them on your own. Your solution should
be submitted as a single script (m-file) in the Ilias system. Each
task should be solved in its own ``cell''. Each cell must be
executable on its own. The file should be named according to the following pattern:
``variables\_datatypes\_\{lastname\}.m'' benannt werden
(e.g. variables\_datentypes\_mueller.m).
\begin{questions}
\question Create vector with the following contents:
\begin{parts}
\part Integer numbers ranging from 1 to 10.
\begin{solution}
\code{a = 1:10;}
\end{solution}
\part Integer numbers in the range 0 to 20 in steps of 2.
\begin{solution}
\code{a = 0:2:20;}
\end{solution}
\part \textbf{Descending} values ranging from 100 to 0.
\begin{solution}
\code{a = 100:-1:0;}
\end{solution}
\part In 10 steps from 0 to 1.
\begin{solution}
\code{a = 0:0.1:1;}
\end{solution}
\part In 11 steps from 0 to 1.
\begin{solution}
\code{a = 0:1/11:1;}
\end{solution}
\part In 50 steps from 0 to $2\pi$ ($\pi$ is known in Matlab as the constant
\code{pi}).
\begin{solution}
\code{a = 0:2*pi/50:2*pi;}
\end{solution}
\end{parts}
\question Calculations with vectors:
\begin{parts}
\part Create a vector \code{x = [3 2 6 8];}
\part What is the size of this vector? Use the functions \code{size} and \code{length}. What is the difference between them?
\begin{solution}
\code{x = [3 2 6 8];
\\ disp(length(x));\\ 4\\ disp(size(x))\\ 1 4}
\end{solution}
\part What changes in \code{size} and \code{length} when you transpose the vector.
\begin{solution}
The length does not change, the size is inverted.
\end{solution}
\part Add 5 to each element of \verb+x+.
\begin{solution}
\code{disp(x + 5)}
\end{solution}
\part Multiply each element of \code{x} with 2;
\begin{solution}
\code{disp(x * 2)}
\end{solution}
\part Create a second vector (\verb+y = [4 1 3 5];+).
Make sure that \code{x} is in its original form.
\part Add both vectors \code{x + y}.
\begin{solution}
\code{y = [4 1 3 5]; \\disp(x + y)\\7 3 9 13}
\end{solution}
\part Subtract \code{y} from \code{x}.
\begin{solution}
\code{disp(x - y)\\-1 1 3 3}
\end{solution}
\part Multiply both vectors \code{x * y}.
\begin{solution}
\code{disp(x * y)\\Error using *. Inner matrix dimension must agree.}
\end{solution}
\part Explain the error message
\begin{solution}
* operator is the matrix multiplication. The inner dimensions must agree.\linebreak
\code{disp(size(x))\\1 4 \\disp(size(y)) \\ 1 4}\\
(m,n)*(n,o) w\"are ok.
\end{solution}
\part What needs to be done to make \code{mtimes} and
\code{*} working?
\begin{solution}
y needs to be transposed: \code{x * y'}
\end{solution}
\part Multiply element-wise (\code{x .* y}) and assign the result to a new variable.
\begin{solution}
\code{z = x .* y;}
\end{solution}
\end{parts}
\question Creating vectors using helper functions:
\begin{parts}
\part Create a vector of the length 100 using the function
\code{ones} (see help). What is its purpose?
\begin{solution}
\code{ones(100,1)} creates a vector of the given size and fills it with 1.
\end{solution}
\part Create a vector of the length 100 using the function
\code{zeros} (see help). What is its purpose?
\begin{solution}
\code{zeros(100,1)} creates a vector of the given size and fills it with 0.
\end{solution}
\part Create a vector with 100 elements. All elements should have the value
4.5.
\begin{solution}
\code{ones(100, 1) * 4.5}
\end{solution}
\part Create a 100 element vector filled with random numbers (\code{rand},
see help).
\begin{solution}
\code{x = rand(100, 1)}
\end{solution}
\part Use the function \code{linspace} to create a 100 element vector with values between 0 and 1.
\begin{solution}
\code{x = linspace(0, 1, 100)}
\end{solution}
\end{parts}
\question Indexing in vectors:
\begin{parts}
\part Create a 100 element length vector with values ranging from 0 to 99.
\begin{solution}
\code{x = linspace(0, 99, 100);}
\end{solution}
\part Print the first, last, fifth, 24th and the second-to-last value.
\begin{solution}
\code{disp(x(1))\\ disp(x(end))\\ disp(x(5))\\ disp(x(24))\\ disp(x(end-1))}
\end{solution}
\part Print the first 10 values.
\begin{solution}
\code{x(1:10)}
\end{solution}
\part Print the last 10 values.
\begin{solution}
\code{disp(x(end-9:end))}
\end{solution}
\part Try to print the value at the zeroth position.
\begin{solution}
\code{x(0)\\ Subscript indices must either be real positive integers or logicals.}
\end{solution}
\part Try to access the value at the 110th position.
\begin{solution}
\code{x(110)\\ Index exceeds matrix dimensions.}
\end{solution}
\part Access the values at the positions 3, 15, and 42 with a single command.
\begin{solution}
\code{disp(x([3 15 42]))}
\end{solution}
\part Access 10 randomly selected values (used \verb+randi+ to create random indices).
\begin{solution}
\code{x(randi(100,10,1))}
\end{solution}
\end{parts}
\question Store some text in a valriable. The text should consist of at least two words (e.g. \code{x = 'some
text'}). Use indexing to print out the words individually.
\begin{solution}
\code{x = 'some text'; \\ disp(x(1:4))\\disp(x(6:end))}
\end{solution}
\end{questions}
\end{document}