1. Systems of Linear Equations
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

2. Infinitely many solutions
Any system of linear equations can be put into matrix form:
Depending on some properties of the matrix A, we can determine what type of solution(s) we should expect.
There are 3 possibilities:
No Solution
If the system is inconsistent there will be no solutions. In this case there will be a contradiction that appears during the solution process. An example is given to the right.
Unique Solution
If the coefficient matrix reduces to the identity matrix there will be a unique (numerical) solution to the system. An example is given to the right.
Infinitely many solutions
If, after row reduction, there are more variables than nonzero rows, the system will have a family of solutions that can be written in parametric form.
An example is given to the right.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB