Sect' 4'8 Using Matrices to Solve Systems of Equations

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Sect. 4.8 Using Matrices to Solve Systems of
Equations
Goal 1 Setting Up Augmented Matrices Goal 2
Solving Systems of Equations Using
Gauss Jordan Elimination
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Augmented Matrix
An augmented matrix contains the coefficient
matrix with an extra column containing the
constant terms.
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Given the following system of equations 3x y
3z 2 2x y 2z 1 4x 2y 5z 5
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Determine the augmented matrix for the system of
equations
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Determine the augmented matrix for the system of
equations
With variables that do not appear in an equation,
we must enter a value of 0 in that spot for our
augmented matrix.
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Gauss Jordan Elimination

• A method used to simplify augmented matrices and
  solve systems of equations.
• The goal is to get leading 1s in our coefficient
  matrix diagonally from left to right.

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How To Solve Using Graphing Calculator
Step 1 Enter augmented matrix into calculator.
5x 6y -47 3x 2y -17
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Step 2 Find the reduced row echelon form
(rref) using the calculator.
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Step 3 Interpret results and define each
variable.
The solution to our system of equations is (-7, 2)
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Solve the system of equations.
5x 3y 13 4x 7y -8
RREF
(5, -4)
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Solve the system of equations.
10x 5y 15 6x 3y -6
RREF
There is no unique solution of this system.
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Solve the system of equations.
3x y 3 6x 2y 6
RREF
No unique solutions. If we check algebraically,
we find there are infinite solutions.