Section 9.4 Systems of Linear Equations: Matrices

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Section 9.4Systems of Linear EquationsMatrices

• Objectives
• Define- matrix, dimension, row, column.
• Find the augmented matrix of a linear system.

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Definition of a matrix

• An m x n matrix is a rectangular array of numbers
  with m rows and n columns.

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• We say the matrix has dimension m x n.
• The numbers amn are the entries of the matrix.
• The subscript on the entry amn indicates that it
  is in the mth row and the nth column.

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Here are some examples.
Matrix Dimension


2 rows by 3 columns
1 row by 4 columns
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Class Work
State the dimension of each matrix. 1. 2. 3.
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Augmented Matrix of a Linear System
We can write a system of linear equations as a
matrix by writing only the coefficients and
constants that appear in the equations. This is
called the augmented matrix of the system.
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Linear System Augmented Matrix

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Ex 1. Write the augmented matrix of the system of
equations.
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Class Work
4. Write the augmented matrix of the system of
equations.
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Ex 2. Write the system of equations for the
given augmented matrix. Then solve the system.
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Ex 3. Write the augmented matrix of the system
and solve the system.
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Class Work
5. Write the augmented matrix and solve the
system.
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Class Work
6. Write the system of equations for the given
augmented matrix. Then solve the system.
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HW p 673 1-6 (state the dimension),15-23 odd, 47
(write the augmented matrix and then solve the
system)