Mathematics, 25.12.2019 01:31, jediDR
The university of texas at austin has three times as many students enrolledas the university of miami. the university of california, berkley has 3,000 more than twice the number of students as the university of miami. if the three schools have a total enrollment of 96,000 students, what is the enrollment at each school?
define the variables in this problem (there are 3 variables).2.write the system of linear equations to represent the scenario.3.write an augmented matrix for the system of linear equations.4.solve the system of equations using your augmented matrix. write down all of the row operations you perform.5.using at least one complete sentence, answer the question: what is the enrollment at each school?
Answers: 2
![\left[\begin{array}{ccc}1&0&-3\\0&1&-2\\1&1&1\end{array}\right]](/tpl/images/0432/3231/76cb1.png)
![\left[\begin{array}{ccc}T\\C\\M\end{array}\right]](/tpl/images/0432/3231/600c8.png)
= ![\left[\begin{array}{ccc}0\\3,000\\96,000\end{array}\right]](/tpl/images/0432/3231/7310e.png)
![\frac{\left[\begin{array}{ccc}0\\3,000\\96,000\end{array}\right]}{\left[\begin{array}{ccc}1&0&-3\\0&1&-2\\1&1&1\end{array}\right]}](/tpl/images/0432/3231/7232b.png)
![\left[\begin{array}{ccc}\frac{1}{2} &-\frac{1}{2} &\frac{1}{2} \\-\frac{1}{3} &\frac{2}{3} &\frac{1}{3} \\-\frac{1}{6} &-\frac{1}{6} &\frac{1}{6} \end{array}\right]](/tpl/images/0432/3231/97af1.png)
is determined by the formula 
. This can also be computed directly on a scientific calculator.![\left[\begin{array}{ccc}46,500\\34,000\\15,500\end{array}\right]](/tpl/images/0432/3231/f718b.png)
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