$2.$ Consider the data generated by the le hw$2$Q$2.$m $($in Matlab$),$ which is assembled into the matrix X$.$ Compute the SVD of X$,$ and plot the first two left singular vectors against y $($the spatial coordinate$).$ Why are the first two singular values much larger than the rest $($which are essentially

zero$)?$

$3.$ Change the function that generates the data in question $2$ so that the spatial peaks $($i$.$e$.$ the Gaussians$)$ change their location with time. How you do this is up to you, so this question is a bit open ended. How does this change the

results of question $2?$ You may also change the amount of data in space and$/$or time if you wish to$.$ clear all

close all

$clc$

dy $=0\mathrm{.}01$;

dy:$2)\text{'}$ ; $\%$spatial coordinate

$dt=0\mathrm{.}2$;

$Nt=101$;

tend $=dt**(Nt-1)$;

$t=0$:$dt$: tend; $\%$time

$\%$ define function

amp$1=1$;

ye$1=0\mathrm{.}5$;

sigmay$1=0\mathrm{.}6$;

amp$2=1\mathrm{.}2$;

$y2=-0\mathrm{.}3$;

sigmay$2=0\mathrm{.}3$;

omega$1=1\mathrm{.}2$;

omega$2=5\mathrm{.}3$;

sigmay$1^22$