Challenge$-1$ Built$-$in functions

MATLAB provides numerous built$-$in variables and functions. For each line below, type the

text in the Command Window and press to see what happens. Is the result what you

expect? Fill in the blanks below with the screen output for that line.

$\%$ Variables, constants, and simple calculations:

a$=250\%$ Look at the Workspace Pane: a VARIABLE called a has been created

a$=901\%$ Look at the variable$$s value in the Workspace Pane

b$=89$

a$/$b $\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

ans

y$=$ ans $\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

x $=2$;

y $=$ x$^$x; z $=$ y$^$y $\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$\%$ Built$-$in functions:

sqrt$($x$)$

pi $\%$ a built$-$in variable

cos$($pi$)\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

abs$($ans$)$

abs$($cos$($pi$))\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

exp$($ans$)$

mod$(7,2)\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ Function rem is similar

help mod $\%$ quick function reference

help rem

doc rem $\%$ detailed function documentation

b$=(4*2)...$

$+1\%$ What does $...$ do$?\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$\%$ It$$s called the ellipsis

Challenge$-2$ for$-$loop

A for$-$loop repeats the loop body$$the statements between the loop header and the end

keyword$$a pre$-$determined number of times. $($The loop header is the line that begins with

the keyword for$).$ What does each loop below do$?$ Write in each blank the output from

executing the loop above.

for a $=2$:$1$:$6$

disp$($a$)\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

end

for b $=2$:$6$

disp$($b$)\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

end

for c $=12$:$0\mathrm{.}5$:$14$

disp$($c$)\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

CT$248$: Introduction to Modelling

Assignment$-1$

end

for d $=0$:$-2$:$-6$

disp$($d$)\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

end

for f $=0$:$-2$:$-7$

disp$($f$)\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

end

for g $=5$:$2$:$1$

disp$($g$)\%$ How many times does the loop body execute? $\_\_\_\_\_\_\_\_$

end $\%$ Any error message? $\_\_\_\_\_\_\_\_$

Challenge$-3$ Vectors

a$=$ zeros$(1,3)\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$=$ ones$(3,1)\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ What do the arguments specify?$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

c$=$ rand$(1,4)\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

d$=10$:$2$:$17\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

f$=10$:$-1$:$7\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

g$=10$:$2$:$0\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

h$=[102040]\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ What does the space separator do$?\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

m$=[10,20,40]\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ What does the comma separator do$?\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

n$=[10$;$20$;$40]\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ What does the semi$-$colon separator do$?\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

p$=[$a h$]\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

q$=[$b; n$]\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

r$=[$a n$]\%$ ERROR$--$mismatched dimensions! $($Attempt to concatenate a column to

$\%$ a row$)$

s$=$ b$\text{'}\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ This operation is called "transpose"

t$=[$a b$\text{'}]\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

u$=$ sum$($t$)\%\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ What does function sum do$?\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

CT$248$: Introduction to Modelling

Assignment$-1$

Challenge$-4$ Determinant of a $3$x$3$ matrix

Write MATLAB code, where x is a $3$x$3$ matrix. Use the following formula:

Use the built$-$in function det$()$ to find the determinant of each $2\backslash$times $2$ matrix. For

example, det$($m$)$ returns the determinant of $2\backslash$times $2$ matrix m$.$ Then use the formula given above

to calculate the determinant of a $3\backslash$times $3$ matrix. This question is all about practicing how to access

individual components or submatrices in a matrix. Recall that you can construct a matrix by

putting two row vectors one below the other or putting two column vectors side by side.