A pseudocode to solve the matrix equation ax $=$ b is given below. Here, a is an n $\backslash$times n matrix and b is an n $\backslash$times $1$ vector. Write a Matlab script $($you must name it GaussEl.m$)$ that uses this pseudocode to find the vector x$.$

Note: Your function will be tested for

$30\mathrm{.}10\mathrm{.}2$ a $=0\mathrm{.}170\mathrm{.}3,$

$0\mathrm{.}30\mathrm{.}210$

$7\mathrm{.}85$

b $=19\mathrm{.}3.(5)$

$71\mathrm{.}4$

Make sure that one gets the correct results when they execute the command

x $=$ GaussEl$([3,-0\mathrm{.}1,-0\mathrm{.}2$;$0\mathrm{.}1,7,-0\mathrm{.}3$;$0\mathrm{.}3,-0\mathrm{.}2,10],[7\mathrm{.}85,-19\mathrm{.}3,71\mathrm{.}4]).$ You do not need to discuss results or the code on your report; make sure enough comments are available in your script.

FUNCTION $[$x$]=$ GaussEl$($a$,$b$)$

n $=$ number of entries in vector b

DOFOR k $=1,$ n$-1$

DOFOR i $=$ k$+1,$ n factor$\_=$ ai$,$k$/$ak$,$k DOFOR j $=$ k$+1,$ n

ai$,$j $=$ ai$,$j $-$ factor$\_$ ak$,$j END DO

bi $=$ bi $$ factor$\_$ bk END DO

END DO

xn $=$ bn$/$an$,$n

DOFOR i $=$ n$-1,1,-1$

sum$\_=$ bi

DOFOR j $=$ i$+1,$n

sum$\_=$ sum$\_-$ ai$,$j $$ xj END DO

xi $=$ sum$\_/$ai$,$i END DO

END GaussEl