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Multivariable Linear Systems

Objective:
In this lesson you learned how to recognize linear systems in
row-echelon form and to use back-substitution to solve the
systems, how to solve systems of equations by Gaussian
elimination, how to solve nonsquare systems of equations,
and how to use systems of linear equations in three or more
variables to model and solve real-life problems.

Important Vocabulary Define each term or concept.

Row-echelon form

Ordered triple

Row operations a

Gaussian elimination

Nonsquare system of equations
I. Row-Echelon Form and Back-Substitution (Page 687)

When elimination is used to solve a system of linear equations,
the goal is. . .

Example 1: Solve the system of linear equations.

What you should learn
How to use back-
substitution
to solve
linear systems in row-
echelon
form
II. Gaussian Elimination (Pages 688-691)

To solve a system that is not in row-echelon form, . . .

List the three row operations on a system of linear equations that
produces an equivalent system of linear equations.

1.
2.
3.

The solution(s) of a system of linear equations in more than two
variables must fall into one of the following three categories:

1.
2.
3,

Example 2: Solve the system of linear equations.

Example 3:
The following equivalent system is obtained
during the course of Gaussian elimination. Write
the solution of the system

What you should learn
How to use Gaussian
elimination to solve
systems of linear
equations
 
III. Nonsquare Systems (Page 692)

In a square system of linear equations, the number of equations
in the system is __ the number of
variables.

If a system has more variables than equations, the system cannot
have a(n) ___ .

Example 4: Solve the system of linear equations.

What you should learn
How to solve nonsquare
systems of linear
equations
 
IV. Applications of Multivariable Systems (Pages 693-694)

The height at time t of an object that is moving in a vertical line
with constant acceleration a is given by the position equation
____ , where s is measured in
feet, t is measured in seconds, v0 is the initial velocity, and s0 is
the initial height.

Describe a situation or application in which solving a system of
multivariable linear systems is required.

Example 5:
Find a quadratic equation, y = ax 2 + b x + c ,
whose graph passes through the points (- 4, 36),
(0, 8), and (2, 0).
What you should learn
How to use systems of
linear equations in three
or more variables to
model and solve
application problems
 

Additional notes

Homework Assignment

Page(s)

Exercises