FABE $3150$

Lab $1-$ MatLab

next week

Sp $24$

For the following exercises, turn in a printout of commands performed in MATLAB and the corresponding results. Also include written comments where necessary.

Calculate

$\sqrt[\phantom{2}]{1\mathrm{.}5{10}^{10}-20i}$

Give answer in short and long scientific notation.

$2.$ Find information on the for command in MATLAB.

$3.$ Generate the following matrix using as few commands as possible:

$E=\left[\begin{array}{cccccc}1& 2& 3& 4& 5& 6\\ 7& 8& 9& 10& 11& 12\\ 13& 14& 15& 16& 17& 0\\ 19& 20& 21& 0& 23& 0\\ 25& 26& 27& 0& 29& 30\end{array}\right]$

Extract the following submatrices:

$F=\left[\begin{array}{cccc}2& 3& 4& 5\\ 8& 9& 10& 11\\ 14& 15& 16& 17\end{array}\right],G=\left[\begin{array}{ccc}1& 2& 3\\ 13& 14& 15\\ 19& 20& 21\end{array}\right]$

Write an m$-$file in MATLAB to do the following:

i$)$ Ask user input for the angle theta $($in degrees$).$ Note angle input on graph.

ii$)$ Compute the following functions shown on the next page.

iii$)$ Plot $f1,f2,$ and $f3$ vs $x$ all on the same figure. Use three different markers and colors to differentiate the curves. Include labels on $x-$axis and $y-$axis, a title, and a legend.

iv$)$ Create a separate figure and plot $f1$ vs $x$ and $f2,f3$ vs $x$ on subplots that are arranged vertically $($i$.$e$.,2$ subplots with one above the other$).$ Use the same markers and colors as above. Include labels for $x-$axis and $y-$axis, a title, and label curves by using the text command.