Examples
MATH 1003 Calculus and Linear Algebra
(Lecture 7)
Maosheng Xiong
Department of Mathematics, HKUST
Maosheng Xiong
Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 7)
Examples
Gauss-Jordan Elimination
In the last lecture, we learned how to solve a system of 2 equations
with 2 variables by performing row operations on its augmented
matrix. Now, we generalize this method so that it can be applied
to any system of linear equations. It is called the
Gauss-Jordan
elimination
.
The idea is very simple: We transform the corresponding
augmented matrix by row operations to a simple form. And the
solution(s) to the linear system corresponding to this simple form
(which is(are) also the solution(s) to the original system) can be
obtained easily.
Maosheng Xiong
Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 7)
Examples
Reduced Form
Definition
A matrix is said to be in
reduced form
if it satisfies
1.
Each row consisting entirely of zeros is below any row having
at least one nonzero element.
2.
The leftmost nonzero element in each row is 1.
3.
All other elements in the column containing the leftmost 1 of
a given row are zeros.
4.
The leftmost 1 in any row is to the right of the leftmost 1 in
the row above.