A student runs a Matlab script which produces the following output:

$>>$ format compact; format rat

$>>$ t $=[-10$; $-1$; $5$; $8]$

t $=$

$-10$

$-1$

$5$

$8$

$>>$ b $=[-10$; $9$; $-8$; $1]$

b $=$

$-10$

$9$

$-8$

$1$

$>>$ m $=$ numel$($t$)$

m $=$

$4$

$>>$ A $=[$ones$($m$,1)$ t$]$

A $=$

$1-10$

$1-1$

$15$

$18$

$>>$ AI $=[$A eye$($m$)]$

AI $=$

$1$

$-101000$

$1-10100$

$150010$

$180001$

$>>$ R $=$ rref$($AI$)$

R $=$

$1$

$0008/3-5/3$

$0100-1/31/3$

$0010-65$

$0001-32$

$>>$ x $=$ A$\backslash$b

x $=$

$-13/6$

$1/3$

$>>$ r $=$ A$*$x$-$b

r $=$

$9/2$

$-23/2$

$15/2$

$-1/2$

$($a$)$

Calculate the matrices

B$=$ATA$=$

$[421$;$2190-10$;$1-101]$

Preview $,$

B$1=$

$[5/7-2/21-5/3$;$-2/211/421/3$;$-5/31/36]$

Preview $.$

$($b$)$

At times ti$,$i$=10,1,5,8$

you are given the values vi

$.$

ti

$10$

$1$

$5$

$8$

vi

$10$

$9$

$8$

$1$

Using the previous part$($s$)$ or the Matlab output, find the line v$=\backslash$alpha $+\backslash$beta t

of best fit to the data

$\backslash$alpha $=$

Number

$\backslash$beta $=$

Number

$.$