Matrices and Systems of Equations

Multiplying matrices may be a challenge for you ... How do I multiply the rows by the columns? How do I add the products? How do I set up the resulting matrix? What is the inverse of a matrix? How can this help me to solve systems of linear equations? ...Augmented Matrix?

One piece of advice: Go through the definitions given at the bottom of the page by scrolling down. This will make easier to follow the lesson. Also, it is important to know that this lesson has been provided with some examples that build onto the transformations that may be done on polygons using compass and ruler, but in this case we use matrices to organize the coordinates and perform some basic operations on matrices to accomplish these same results of translating, reflecting, or rotating polygons in the coordinate plane. The MARKER TOOLS menu located on the top of the screen has some useful features like highlighter, and pen that you may use to mark important sections in the lesson or write useful notes to come back using the navigability provided by the thumbnails on the left of the screen. Fortunately for you this lesson takes a great deal in addressing the questions asked in the beginning of this narrative, and of many other ones. It uses your natural ability to follow the flow of events by highlighting each step with colors, and keeping track of what has been done. You will really find it easy to understand and apply to more problems you may later encounter.

Lesson's Content

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Lesson In PDF Format (no animations)

Lesson's Glossary

Determinant for matrix 2x2:

matrix

2 by 2 Matrix

has determinant

2 by 2 Determinant
 
Determiant for matrix 3x3:

matrix

        3 by 3 Matrix

has determinant

3 by 3 Determinant

 

Equivalent system:  A system of equations having the same solution set as another system.

Graph of an equation in two variables:  All the points that may be graph from the solution set of the equation.

Graph of a function:  The solution set graphed for the function in the given domain.

Graph of a number:   The location of a point paired with a number in the number line.

Graph of an ordered pair:  The location in the coordinate plane associated with an ordered pair of real numbers.

Linear equation:   Any equation with all exponents = 1 regardless of the form the equation is represented.

Linear equation in two variables:   All equivalent equations to the one in the form of ax + by = c, where a, b, and c are in the set of the real numbers and a and b can't be zero at the same time. The graph is a straight line.

Linear function:  A function of the form: f(x) = mx + b.

Matrix: Rectangular arrangement of numbers in rows and columns that uses large brackets in order to define the matrix. A matrix size is defined by number of rows and number of columns.

Ordered pair:   In a coordinate plane is the location of a point.

Slope of a line:The measure of how steep a line is. The change in y (rise) divided by the change in x (run). Slope = m

Slope-intercept form of an equation:   The equation of a line in the form y = mx + b, where m represents the slope, and be represents the y-intercept.

Solution of an equation in two variables:  Any ordered pair of real numbers that makes the sentence true.

Solution of a system of two equations in two variables:   Ordered pair that when replaced in the equations produces a true statement for both equations.

Solve a system of two equations in x and y:   Finding all ordered pairs (x,y) which make both equations in the system true.

Standard form of a linear equation:   ax + by = c, where a, b, and c are integers and a and b are not both zero.

 

 

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