1.1 Linear Algebra

When is a row equivalent?

Two linear systems are considered row equivalent if they can be transformed into each other through a series of elementary row operations.

they have the same solution set. Each solution of the first system is a solution of the second system, and each solution of the second system is a solution of the first

What is a system of linear equations/linear system?

a collection of one or more equations involving the same set of variables.

What is A SOLUTION of the system?

A specific set of values for the variables that satisfies all equations in the system. a list of numbers that makes each equation a true statement when substituted.

what is a SOLUTION SET?

The set of all possible solutions to a system of linear equations, representing values that satisfy each equation in the system. Each solution of the first system is a solution of the second system, and each solution of the second system is a solution of the first.

When is a system of linear equations consistent?

the system has

1. ONE SOLUTION

2. INFINITELY MANY SOLUTIONS

lines in the graph crosses or overlaps

When is a system of linear equations inconsistent?

1. NO SOLUTION

lines in the graphs are parallel and never meet!