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Systems of Equations in Three Variables

Systems of Equations in Three Variables

Author: Kristel Sortelli
Description:

You will use technology and algebra to solve systems of linear equations in three variables.

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Tutorial

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Using the Calculator:

What do the A and B represent? The letters A and B are capitalized because they refer to matrices. Specifically, A is the coefficient matrix and B is the constant matrix. In addition, X is the variable matrix. No matter which method you use, it’s important to be able to convert back and forth from a system of equations to matrix form.

Example: Be sure to follow this example using your calculator. 

This is how the matrices would be set up.


Just follow these steps:

1.  Enter the coefficient matrix, A.  Press left square bracket A L P H A right square bracket left square bracket Z O O M right square bracket to create a matrix from scratch or press left square bracket 2 n d right square bracket left square bracket x to the power of negative 1 end exponent right square bracket to access a stored matrix. See the first screen below.  Make sure that Matrix A is set as a 3 x 3.

2.  Press [x to the power of negative 1 space end exponent] to find the inverse of matrix A.  See the second screen below.

3.  Enter the constant matrix, B.  Press left square bracket A L P H A right square bracket left square bracket Z O O M right square bracket to create Matrix B.  See the third screen below.  Make sure that Matrix B is set as a 3 x 1.

4.  Press left square bracket E N T E R right square bracket to evaluate the variable matrix, X.  The variable matrix indicates the solutions: x = 5, y = 0, and z = 1. See the third screen below.  Remember that the answers for each variable will go in order - x, y, z.

Practice:

Practice assignment w/ answer key

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