A university admissions committee anticipates an enrollment of 8,000 students in its freshman class next year. To satisfy admission quotas, incoming students have been categorized according to their sex and place of residence. The number of students in each category is given by the matrix By using data accumulated in previous years, the admissions committee has determined that these students will elect to enter the College of Letters and Science, the College of Fine Arts, the School of Business Administration, and the School of Engineering according to the percentages that appear in the following matrix: Find the matrix AB that shows the number of in-state, out-of-state, and foreign students expected to enter each discipline.

Question

A university admissions committee anticipates an enrollment of 8,000 students in its freshman class next year. To satisfy admission quotas, incoming students have been categorized according to their sex and place of residence. The number of students in each category is given by the matrix  By using data accumulated in previous years, the admissions committee has determined that these students will elect to enter the College of Letters and Science, the College of Fine Arts, the School of Business Administration, and the School of Engineering according to the percentages that appear in the following matrix:  Find the matrix AB that shows the number of in-state, out-of-state, and foreign students expected to enter each discipline.

Quizplus · Accepted Answer

We need to multiply the two given matrices (number of students in each category and percentage of students entering each discipline) to get the desired matrix AB that shows the number of in-state, out-of-state, and foreign students expected to enter each discipline. The resulting matrix will have 3 rows (one for each type of student) and 4 columns (one for each discipline). Each element in the resulting matrix will be the sum of the products of the corresponding row in the first matrix and corresponding column in the second matrix.

Using matrix multiplication, we get:

AB = 11eab448_e873_f5f6_acdb_2f77d90c23f4_TB6027_11

Therefore, the best choice is option C.

A University Admissions Committee Anticipates an Enrollment of 8,000 Students