1. Systems of Linear Equations: Matrices
Section 11.2
Systems of Linear Equations: Matrices
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2. Write the augmented matrix of a system of linear equations.
Objectives
Write the augmented matrix of a system of linear equations.
Perform row operations on a matrix.
Solve a system of linear equations using matrices.
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3. You already know two methods for solving a system of equations.
Substitution and elimination
Another approach to the elimination method is to use matrices.
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4. The matrix used to represent a system of linear equations is call an augmented matrix.
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5. Write the augmented matrix of each system of equations.
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6. If the constants are not included, the resulting matrix is called the coefficient matrix.
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7. Row operations can be used to solve a system of equations written as an augmented matrix.
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10. The advantages of solving a system of equations this way are
To solve a system of linear equations using matrices, we use row operation son the augmented matrix of the system to obtain a matrix that is in row echelon form.
The advantages of solving a system of equations this way are
The process is algorithmic meaning that a computer can perform the repetitive steps.
The process works for any number of variables or equations.
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14. The good news is that the calculator can do this for you!
To enter the matrix into the calculator:
MATRIX (2nd x‒1)
EDIT: enter # by # and entries
To get row echelon form:
MATRIX
MATH
A: ref( )
(You can display the answers and fractions using ►FRAC if you prefer.)
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17. Reduced Row Echelon Form
Reduced row echelon form is even better because the solution is given without having to substitute.
The method to get a matrix in this form is called Gauss-Jordan elimination.
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18. The calculator can do this too!
MATRIX
MATH
B:rref( )
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21. The system is inconsistent.
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24. Homework
11.2
#5, 7, 13, 15, odd
#37, 47, 51, 59 (with calculator)
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