Engineering H192 - Computer Programming
MATLAB: Simultaneous Equations
Lecture 22
Winter Quarter Gateway Engineering Education Coalition Lect 22 P. 1

Engineering H192 - Computer Programming
Simultaneous Equations with MATLAB
• MATLAB is very powerful for solving systems of N equations with N unknowns. It is used extensively for analyzing electric power grids and circuits, fluid flow in piping systems, and other engineering applications. It can, of course, be used for any application with n equations and n unknowns.
• For example, suppose that a Calculus text (C), a Physics text (P) and a Graphics text (G) can be purchased for $146.
Then suppose the Calculus and Graphics texts can be purchased for $87 and the Physics and Calculus texts can be purchased for $105. How much does each text cost?
Winter Quarter Gateway Engineering Education Coalition Lect 22 P. 2

Engineering H192 - Computer Programming
Simultaneous Equations with MATLAB
• The problem can be written as:
1P + 1C + 1G = 146
1C + 1G = 87
1P + 1C = 105
>>Books=[1,1,1;0,1,1;1,1,0]
Books =
1 1 1
0 1 1
1 1 0
• In MATLAB, the coefficients of the variables P, C & G are placed in a matrix and the
Dollar values in a column vector.
>>Dollars=[146;87;105]
Dollars =
146
87
105
Winter Quarter Gateway Engineering Education Coalition Lect 22 P. 3

Simultaneous Equations with MATLAB
• Now, the inverse of the matrix Books is multiplied by the vector Dollars:
>>Cost = inv (Books) * Dollars
Cost =
59
46
41
• This vector contains the cost of P in row one, C in row 2 and G in row 3.
Winter Quarter
Engineering H192 - Computer Programming
Gateway Engineering Education Coalition Lect 22 P. 4

Engineering H192 - Computer Programming
Simultaneous Equations with MATLAB
• Another MATLAB solution would be to use the reverse division sign as follows:
>>Cost = Books \ Dollars
Cost =
59
46
41
Winter Quarter Gateway Engineering Education Coalition Lect 22 P. 5

Engineering H192 - Computer Programming
Simultaneous Equations with MATLAB
• A third MATLAB solution can be obtained by using the Row Reduced Echelon Form (rref) function as follows. First combine the matrix and vector:
EDU» COMBINED=[Books Dollars]
COMBINED =
1 1 1 146
0 1 1 87
1 1 0 105
Winter Quarter Gateway Engineering Education Coalition Lect 22 P. 6

Engineering H192 - Computer Programming
Simultaneous Equations with MATLAB
• Then invoke the rref function with the resulting matrix.
>> Cost = rref (COMBINED)
Cost =
1 0 0 59
0 1 0 46
0 0 1 41
• The last column in the new matrix is the cost vector.
Winter Quarter Gateway Engineering Education Coalition Lect 22 P. 7