Linear First Class

only typed notes first day

1.1 Systems of Linear Equations

$a_1{x}_1+a_2{x}_2+...+a_n{x}_n=b$ (this)

a = coefficients, x = variable ~~~ example of a system is like y = mx+b (line)

if any term was squared, it would not be linear

if two variables are multiplied, it would not be linear

how do you solve something like ^

solution ($s_1,...s_n$) - makes all the equations true

solution set - all solutions

equivalent systems of linear equations (SOLE) have the same solution set

A system of linear equations has 0, 1, or infinite solutions

if it has 0 it is inconsistent, else: consistent

Solve a system of linear equations:

you can:

• multiply an equation by coefficient (for cancelling)
• add/subtract rows (equations)

**matrix (m x n), (rows x columns)

imagine the ’|’ as the equals sign of the system of linear equations

line coefficients in a matrix (literally how you see them) | constants

Elementary Row Operations

1. Replacement - add a multiple of one row to another
2. Interchange - swap two rows
3. Scaling - multiply a row by a nonzero constant