10.2 Day 3 Systems of Linear Equations ­ Matrices 2010 December 08, 2010
10.2 Systems of Linear Equations: Matrices Day 3
Objectives:
1. Write the augmented matrix of a system of linear equations. 2. Write the system from the augmented matrix.
3. Perform row operations on a matrix.
4. Solve a system of linear equations using matrices. Nov 9­12:20 PM
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10.2 Day 3 Systems of Linear Equations ­ Matrices 2010 December 08, 2010
Warm­up:
Given reduced row echelon form write the system of equations corresponding to the given matrix. Is the system consistent or inconsistent? If consistent, give the solution.
1.
[ ] [ ]
1 0 0 ­8
0 1 0 5
0 0 1 0
2.
1 0 ­3 4
0 1 2 7
0 0 0 0
Dec 6­12:13 PM
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10.2 Day 3 Systems of Linear Equations ­ Matrices 2010 December 08, 2010
Dec 8­12:27 PM
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10.2 Day 3 Systems of Linear Equations ­ Matrices 2010 December 08, 2010
Ready?
...time to put it all together!!
Nov 30­12:40 PM
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10.2 Day 3 Systems of Linear Equations ­ Matrices 2010 December 08, 2010
Solve a System of Linear Equations Using Matrices Example #1: Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
{
Step 1: Write the system as an augmented matrix.
2x + 2y = 6
x + y + z = 1
3x + 4y ­ z = 13
Step 2: Use row operations to change into row echelon form.
HINT: Start with the first column.
Step 3: Solve for each variable.
Answer:
x = 1, y = 2, z = ­2
Nov 30­12:40 PM
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10.2 Day 3 Systems of Linear Equations ­ Matrices 2010 December 08, 2010
Solve a System of Linear Equations Using Matrices {
Example #2: Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
4x ­ 3y + 5z = 0
2x + 4y ­ 3z = 0
6x + 2y + z = 0
Answer:
1
z, y = z, z = any real number
x = ­ 2
Nov 30­12:40 PM
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10.2 Day 3 Systems of Linear Equations ­ Matrices 2010 December 08, 2010
Solve a System of Linear Equations Using Matrices Example #3: Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
{
x + y + z = 6
2x ­ y ­ z = 3
x + 2y + 2z = 0
Answer:
Inconsistent
Nov 30­12:40 PM
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10.2 Day 3 Systems of Linear Equations ­ Matrices 2010 December 08, 2010
Homework: page 754 (37 ­ 59 odd) Nov 30­12:40 PM
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