Gaussian Elimination: a systematic way of solving the system
not always possible, when impossible, get Row Echelon Form
always reaches echolon form
If the number of equations equals the number of variables, the system in non-singular
Pivot: leading coefficients
(Row) Echelon Form (ref):
Rows at the form (0, ..., 0 | x) are at the bottom if exists
any pivot cutting is in a column to the left from any pivot below it // QUESTION: WHAT? Explain? pivot of a nonzero row is always strictly to the right of the leading coefficient of the row above it.
If the system is non-singular: Echolon Form is Triangular
If the system is singular: at least one (0, ..., 0 | x) (but the opposite is not true)
Reduced Row Echelon Form (rref): if furthermore all of the leading coefficients are equal to 1
Canonical Form: can be viewed as solution
Triangular System: special Echelon Form which indicate exactly one solution
where \circ represent non-zero, and x can be zero or non-zero
If a system has infinite many solution, pick the variable that is not in Row-reduced form, then subsitute that with variable constant P, solve for P.
A by B matrix
a number of equation
b number of variables
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