Module 2: Systems of Equations and Inequalities Liberty Carter by Liberty Carter

Vocabulary

carterl9017 — 2016-10-04 18:57:13 UTC

Matrix: a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
Augmented Matrix: a matrix obtained by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on each of the given matrices.
Reduced Matrix: a matrix is in reduced row echelon form if it satisfies the following conditions: every leading coefficient is 1 and is the only nonzero entry in its column.
Feasible Region: an area defined by a set of coordinates that satisfy a system of inequalities.
Max Profit: when the amount of revenue gained from a business activity exceeds the expenses.
Constraints: a condition of an optimization problem that the solution must satisfy.

Row Reduction

carterl9017 — 2016-10-04 19:09:05 UTC

To put a augmented matrix into reduced row-echelon form. A matrix is in reduced row-echelon form if it meets all of the following conditions: If there is a row where every entry is zero, then this row lies below any other row that contains a nonzero entry. The leftmost nonzero entry of a row is equal to 1.

Row Reduction Rules

carterl9017 — 2016-10-04 19:14:15 UTC

- You can switch any rows
- You can scalar any row
- You can add and subtract rows
- You can scalar and add/subtract at the same time
- Column 1 is x and Column 2 is y.

Example:

carterl9017 — 2016-10-05 22:05:42 UTC

How To Graph 2 Variable Inequalities

carterl9017 — 2016-10-06 01:20:30 UTC

-Explains how to graph a line with Slope Intercept Form.
-Goes over how to visually show all the signs; <, >, <=, and >= on a graph.
-Explains what said signs mean.

Row Reduction Steps

carterl9017 — 2016-10-06 01:33:56 UTC

1. Put the given equations into an augmented matrix:
[# # | #]
[# # | #]
2. Make either the x and y values of Row 1 and Row 2 the same
3. Subtract Row 1 and Row 2
4. Dived to create a value of 1 in one of the rows
5. Repeat steps 1-3 for the other x/y value
6. The finished matrix should be a reduced matrix:
[1 0 | #]
[0 1 | #]

Graphing Inequalities With Constraints

carterl9017 — 2016-10-06 01:50:11 UTC

Graphing inequalities on either a number line or in the coordinate plane helps to visually represent several forms of inequalities:
The graph of a linear inequality produces a region on the coordinate plane with a boundary line. Every point in that region is a solution of the inequality. With multiple inequalities (constraints) the region where they all intersect is the feasible region.

Example:

carterl9017 — 2016-10-06 02:16:57 UTC