$(1$ point$)$ The BCS ranking system was more complicated in $2001$ than in $2008.$ The table below gives the BCS rankings at the end of the regular season. $($A lower BCS Index gave a higher rank.$)$

Table headings:

AP and USA gives the rank of each team in two opinion polls of writers and coaches, respectively.

SS stands for strength of schedule ranking, with $1$ being the most challenging.

L is the number of losses during the season.

CA $($Computer Average$)$ is the average of computer rankings from various sources.

QW $($Quality Wins$)$ gives a measurement of the number of victories over highly ranked teams.

Rank$123456789101112131415$TeamMiamiIllinoisTennesseeLSUNebraskaSouth CarolinaColoradoStanfordOregonWashington StOklahomaMarylandFloridaTexasWashingtonAP$178124143112131065716$USA$178124143112131065721$SS$1837410134022430453674193521$L$012313221221223$CA$1\mathrm{.}059\mathrm{.}736\mathrm{.}07132\mathrm{.}05194\mathrm{.}467\mathrm{.}764\mathrm{.}8110\mathrm{.}838\mathrm{.}9411\mathrm{.}035\mathrm{.}786\mathrm{.}7614\mathrm{.}76$QW$0\mathrm{.}201\mathrm{.}510\mathrm{.}802\mathrm{.}31\mathrm{.}20\mathrm{.}80\mathrm{.}90\mathrm{.}800\mathrm{.}81\mathrm{.}11$BCS Index$2\mathrm{.}542\mathrm{.}965\mathrm{.}316\mathrm{.}347\mathrm{.}117\mathrm{.}367\mathrm{.}377\mathrm{.}828\mathrm{.}618\mathrm{.}9710\mathrm{.}8611\mathrm{.}8513\mathrm{.}0414\mathrm{.}4338\mathrm{.}09$

Find a formula for the $2001$ BCS ranking. $($Instructions: What you are expected to do is choose the data from $6$

of the schools to form a system of $6$

equations in $6$

unknowns x$1,$x$2,,$x$6$

$.$ Normally one might think the best idea would be to choose the six top schools but if you try that it will not work because the coefficients for the x$1$

and x$2$

are the same for each of the six schools, and thus Gaussian Elimination leads to $0=1$

$,$ which is absurd$.$ So use the first five schools and Washington and you will be able to obtain a unique solution.$)$

BCS Index $=$

$($AP$)+$

$($USA$)+$

$($SS$)+$

$($L$)+$

$($CA$)+$

$($QW$)$