Question

• Do the calculations on Matlab, print it out and then write your answers on the attached answer

sheet.

• Attach your Matlab printout to your answer sheet before you hand in.

1. Find all solutions for each of the following systems of equations (if the system is consistent):

(a) 6.5x − 2y = 7 (b) 3.5x1 + 4.5x2 + 5.5x3 = 11

2x − 0.75y = 1.75 x1 + 4x2 − 7x3 = −16

12x − y = 21 0.5x1 − 0.75x2 + 0.75x3 = 3.5

(c) − 0.75x1 + 0.75x2 = −6

2.5x1 + 2x2 − 4.5x3 = 2

1.25x1 + 1.25x2 − 2.5x3 = 0

(d) 3.4x1 + 3.4x2 − 15.3x3 = −20.4

0.5x1 + 0.25x2 − 0.75x3 = 1

0.75x1 + 0.5x2 − 1.5x3 = 1

Please note: You should use Matlab to write your systems in reduced row echelon form, but have to

interpret the results and give the solution(s) if the system is consistent.

Answer 1

(a)

>> A = [6.5 -2
     2 -0.75
     12 -1];
A(:,3) = [7; 1.75; 21];
R = rref(A)
R =
     1     0     2
     0     1     3
     0     0     0

The system has a unique solution:

x=2; y=3

(b)

>> A = [3.5 4.5 5.5
     1 4 -7
     0.5 -0.75 0.75];
A(:,4) = [11; -16; 3.5];
R = rref(A)
R =
    1.0000         0         0    2.1840
         0    1.0000         0   -1.4303
         0         0    1.0000    1.7804

The system has a unique solution:

x1=2.1840; x2=-1.4303; x3=1.7804

(c)
>> A = [-0.75 0.75, 0
   2.5 2 -4.5
   1.25 1.25 -2.5];
A(:,4) = [-6; 2; 0];
R = rref(A)
R =
    1    0   -1    4
    0    1   -1   -4
    0    0    0    0

The system has multiple solutions:

x1=x3+4; x2 = x3-4

(d)

>> A = [3.4 3.4 -15.3
    0.5 0.25 -0.75
    0.75 0.5 -1.5];
A(:,4) = [-20.4; 1; 1];
R = rref(A)
R =
     1     0     0     4
     0     1     0     8
     0     0     1     4

The system has a unique solution:

x1 = 4; x2 = 8; x3 = 4