Question

5. A College has 1200 students, studying in Diploma I, Advance Diploma and Bachelor are conducted, allotted for the Students of Diploma - I is 3 hours, Advance Dipl oma requires 1 hour and Bachelor requires 2 hours. Invigilation cost for the exam is $12 per hour. Exam material costs are $10 per for Diploma - I, $15 per for Advance Diploma and $5 per for The Management the Exams time When the Bachelor has planned to spend $24,000 on Invigilation charges and $13,000 on Venue. (Each bit carries 0.2 M) (a) Use Mathematical Code to define the linear equations into the Matrix form and write the matrices and with the augmented matrix in the output. Code to evaluate the upper (b) Use MATLAB triangular matrix of matrix A (c) Check whether the matrix is symmetric using MATLAB SUBSCRIPT (d) Use MATLAB Code to check whether: a. b. (e) Use MATLAB Code to find the numbers of students in each group are able to write the exam?

Answer 1

Solution:

a) Let  
1
and  $x_3$ be the number of students studying in Diploma, Advance Diploma and Bachelor respectively. Total number of students are 1200. So the first equation we get is,

T1 2 3 = 1200

The management has planned to invest 24000 on invigilation costing 12 per hour. so we have in total 24000/12 =  2000 hour. Time allotted for diploma is 3 h , advance diploma is 1 h and bachelor is 2 h respectively. so the equation we get is

3r1 22.x3 = 2000

The management has planned to invest 13000 on venue which includes the material cost so the third equation is

10x1152+5x3= 13000

2.132x3=2600

So the linear system of equation for this problem is,

AX B [1200] and B 2000 1 1 1 A =3 1 2 X|2 2 3 1 2600

The Augmented matrix is,

1 1 1200 3 1 2 2000 2 3 1 2600

b) Upper Triangular matrix of matrix A using matlab code,

triu(A);

c) Checking matrix is symmetric or not in matlab,

n=3;

A = [1 2 3; 2 4 5; 3 5 6];

flag = 1;

for i = 1:n

for j = 1:n

if(A(i,j) == A(j,i))

continue;

else

flag = 0;

break;

end

end

if(flag == 0)

fprintf('Not Symmetric Matrix');

break;

end

end

if(flag == 1)

fprintf('Symmetric Matrix');

end

Using Built in matlab function:

  tf = issymmetric(A);

if(tf == 1) printf("symmetric");

else printf("Not Symmetric");