Answer:
University of Texas has 46,500 students, University of California has 34,000 students and University of Miami has 15,500 students.
Explanation:
Represent Texas with T, Miami with M and California with C. With the given information, the following equations were obtained.
T = 3 × M
T – 3M = 0 ………………………….(i)
C = 3,000 + 2 × M
C – 2M = 3,000…………………..(ii)
T + C + M = 96,000…………….(iii)
By rearranging, we have:
1T + 0C – 3M = 0 ………………………….(i)
0T + 1C – 2M = 3,000…………………..(ii)
1T + 1C + 1M = 96,000………….…….(iii)
The Augmented Matrix is:
=
Making the subject of the formula we have:
=
Let’s say matrix A = , the inverse of matrix A = is determined by the formula . This can also be computed directly on a scientific calculator.
=
=
T = 46,500
C = 34,000
M = 15,500
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