Linear Systems

Solving linear systems

• identify unknowns

• write linear equations describing relationships between unknowns

   

   

   

• convert equations to general form

• rewrite as Ax = b

   

   

   

   

Using MATLAB

• create coefficient matrix A

• create data vector b

• solve:

   

   

If A is square, will there be a solution?

If A is non-singular, then

If A is singular, then

either system is redundant

or system is inconsistent

In either case

Component analysis

Four roommates purchased school supplies and decided to compare notes. They didn't keep their receipts; they just knew the total amount and what they bought (we'll ignore sales tax issues):

• Roommate 1 got 4 pencils, 2 pens, and 3 notebooks for $8.55
• Roommate 2 got 3 pens and a notebook for $3.42
• Roommate 3 got 3 pencils, 1 pens, and 2 notebooks for $5.65
• Roommate 4 got 2 pencils and a notebook for $3.17

Roommate 4 feels overcharged. Can we determine whether roommate 4 was charged the correct amount?

Traffic flow

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

Heat plate

The temperature of a given square is the average of the squares around it.