Row Echelon Form Lesson

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In this section, we continue to learn about Gaussian Elimination. Our goal is to place a matrix in row echelon
form and obtain the solution to a linear system of equations. We will now move on and look at systems with three
equations and three variables (x, y, and z). To use a matrix to solve a linear system, we would write each equation
in standard form and then list the numerical information (coefficients and constants only) inside of a matrix.
The matrix will have brackets on the outside. The matrix we will construct will have a vertical line to separate
the coefficients from the constants. This type of matrix is known as the augmented matrix. We can manipulate the
matrix using row operations. The following are row operations: 1) We can interchange any two rows, just like we can
switch the order of which equation is on top and which equation is on the bottom. 2) We can multiply any row by a
non-zero number, just like we can multiply any equation by a non-zero number and not change the solution. 3) We can
multiply a row by a real number and add this to the corresponding elements of any other row. We will use these row
operations to produce a matrix that is in row echelon form. This gives us 1’s down the diagonal and 0’s below. In this
form, we are given one unknown, and can use substitution to find the other. Additionally, we can work further in the
matrix and place it into reduced row echelon form. This form gives us all solutions without any further work. Reduced
row echelon form gives us 1’s down the diagonal and 0’s above and below.

Row Echelon Form Resources:

Videos:

Khan Academy - Video
Patrick JMT You-Tube - Video
My Why U - YouTube - Video
Text Lessons:

Cliffs Notes - Text Lesson
HMC EDU - Text Lesson
Purple Math - Text Lesson
Worksheets:

Online Math 4 All - Worksheet
LAVC EDU - Worksheet
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