Two subjects, Pure Mathematies and Applied Mathematics, are offered in the first semester of auniversity science course.The matrix N lists the number of students enrolled in each subject.540Pure360 AppliedThe matrix G lists the proportion of these students expected to be awarded grades 4, B, C, D or Ein cach subject.A B C D EG=[ 0.05 0.125 0.175 045 0.20 ]a.Write down the orders of matrices N and G.The final results matrix (R) shows the final number of students achieving each grade foreach Mathematics subject, and is calculated as follows : R= NG.b.i.Evaluate the matrix R, showing results correct to the nearest integer.ii.Explain what the matrix element R13 represents.If an E grade is considered a fail, how many students, in total, will have failed theseii.subjects at the end of the semester.Students enrolled in Pure Mathematics have to pay a course fee of $110, whilestudents enrolled in Applied Mathematics pay a course fee of $150. These course fees coverthe course of printed notes and access to a variety of resources.i.Write down a clearly labelled row matrix, called F, that lists these fees.ii.Show a matrix calculation that will give the total course fees, C, paid indollars by the students enrolled in Pure and Applied Mathematics.Find this amount. The following transition matrix, 7, is used to help predict class attendance of Pure Mathematicsstudents at the university on a lecture-by-lecture basis.this lectureattend not attendT- 085 0.250.15 0.75attendnext lecturenot attendSo is the attendance matrix for the Pure Mathematics information session.510attend30not attendSo indicates that 510 Pure Mathematics students attended the information session and 30 PureMathematics students did not attend the information session.d. Use T'and So toi.determine S1 the attendance matrix for the first lecture, writing youranswers correct to the nearest integer.ii.predict the number of Pure Mathematics students attending the third lecture,writing your answer correct to the nearest integer.Write down a matrix equation for S, in terms of T, n and So, that would enable us to predictthe number of students attending any of the 52 lectures scheduled for Pure Mathematies inSemester One.To cut down on cleaning costs, the Pure Mathematics lecture will be transferred to a smaller lecturetheatre when the number of students predicted to attend falls below 350.1. For which lecture can this first be done?Predict, correct to the nearest integer, the number of students who will be attendingthe Pure Mathematies lectures :i.one-quarter of the way through the courseii.one-half of the way through the course

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In the question we have to find matrixes. 
 
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