Linear Systems

Solving linear systems

• identify unknowns

   

• write linear equations describing relationships between unknowns

   

   

   

• convert equations to general form

   

   

• rewrite as Ax = b

   

   

   

   

   

To solve in MATLAB

1. Create coefficient matrix A
2. Create right-hand side column vector b
3. Solve using \

Will there be a solution?

Examples

Traffic flow

Traffic flow into an intersection must equal the traffic flow out of an intersection.

Component analysis

A juice company manufactures one-gallon bottles of three types of juice blends using orange, pineapple, and mango juice. The blends have the following compositions:

• 1 gallon orange blend: 3 quarts of orange juice, 0.75 quart of pineapple juice, 0.25 quart of mango juice
• 1 gallon pineapple blend: 1 quart of orange juice, 2.5 quarts of pineapple juice, 0.5 quart of mango juice
• 1 gallon mango blend: 0.5 quart of orange juice, 0.5 quart of pineapple juice, 3 quarts of mango juice

How many gallons of each blend can be manufactured if 7,600 gallons of orange juice, 4,900 gallons of pineapple juice, and 3,500 gallons of mango juice are available? (Note that 1 gallon = 4 quarts)