Linear Algebra Lecture 3.

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Presentation transcript:

Linear Algebra Lecture 3

Systems of Linear Equations

Examples of Linear Equations

Generally An equation in n-variables or in n-unknowns

Homogenous Linear Equations If b=0

Examples of Linear Equations

Non Linear Equations

Linear System A finite set of linear equations is called a system of linear equations or linear system. The variables in a linear system are called the unknowns.

Linear System

Theorem Every system of linear equations has zero, one or infinitely many solutions; there are no other possibilities.

Example

Example (answer)

Matrix Notation

Matrix Notation Matrix of Coefficients

Example Solve

Example Test the Consistency

Example Test the Consistency

Example (Solution) Inconsistent ! So: NO SOLUTION

Linear Algebra Lecture 3