SOLVING SYSTEMS MATRICES -...
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3_Solving_Systems_Matrices_Final_16.notebook 1 March 21, 2016 SOLVING SYSTEMS MATRICES Teachers' notes Lesson objectives 1) Solve systems using Gaussian Elimination, Reduced Row Echelon Form, graphing calculators, and augmented matrices.
Transcript of SOLVING SYSTEMS MATRICES -...
3_Solving_Systems_Matrices_Final_16.notebook
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SOLVING SYSTEMSMATRICES
Teachers' notesLesson objectives
1) Solve systems using Gaussian Elimination, Reduced Row Echelon Form, graphing calculators, and augmented matrices.
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Lesson objectives Teachers' notes
Subject:
Topic:
Grade(s):
Prior knowledge:
Crosscurricular link(s):
PreCalculus Honors
Systems and Matrices
1012
basic matrix operations
biology, business, science
Lesson notes:
Type text here
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SOLVING SYSTEMS MATRICESVOCABULARY
Gaussian elimination – a method used to transform a system of equations into triangular form. Named after German mathematician Carl Friedrich Gauss (1777 1855).
Augmented Matrix – a matrix used to represent a system of linear equations.
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Row Operation – on an augmented matrix any of the following: switch two rows, multiply a row by a constant, add one row to another.
Row Echelon Form – using row operations to obtain triangulation of the matrix. When the matrix is in reduced row echelon form the solutions are obtained.
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An Augmented Matrices
EX #1: Write the augmented matrix.
A.
B.
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An Augmented Matrix
EX #2: Write the system of linear equations represented by the augmented matrix. Use variables x, y, and z.
A.
B.
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Applying Row Operations on Matrices
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Operations Using Matrices
EX #3: Using the matrix below, find a row operation for the following:
A. Having a 0 in row 1, column 2.
B. Having a 0 in row 2, column 1.
C. Having a 1 in row 2, column 2.
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Solving a System Using Matrices
EX #4: Given
A. Write the augmented matrix.
B. Perform the indicated row operations. State the solution.
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Solving a System with Three Variables
EX #5: Solve using row operations.
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Solving Systems with Inverse Matrices
EX #6:
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Analyzing a Network EX #7: Network analysis is important in computer science. In a network, it is assumed that the total flow into a junction (each circle) is equal to the total flow out of the junction. Set up a system of linear equations representing the network below. Solve the system using the capabilities of a graphing utility.
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Let A be a square n x n matrix. If there exists an n x n matrix A1 , read “A inverse,” where
Then A1 is called the inverse of matrix A.
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Find an Inverse Matrix with a Calculator
EX #7: Find the inverse of matrix A.
With the TIInspire, pick the template and set the matrix size:
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Enter the elements in each row and column:
Calculate the inverse:
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EX #8: Now verify that
Find an Inverse Matrix with a Calculator
