10.2 Day 3 Systems of Linear Equations - Matrices 2010
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10.2 Day 3 Systems of Linear Equations Matrices 2010 1 December 08, 2010 Nov 912:20 PM 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.
Transcript of 10.2 Day 3 Systems of Linear Equations - Matrices 2010
10.2 Day 3 Systems of Linear Equations Matrices 2010
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December 08, 2010
Nov 912:20 PM
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.
10.2 Day 3 Systems of Linear Equations Matrices 2010
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December 08, 2010
Dec 612:13 PM
1. 2.
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 0 0 80 1 0 50 0 1 0 [ ]1 0 3 4
0 1 2 70 0 0 0
10.2 Day 3 Systems of Linear Equations Matrices 2010
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December 08, 2010
Dec 812:27 PM
10.2 Day 3 Systems of Linear Equations Matrices 2010
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December 08, 2010
Nov 3012:40 PM
Ready?...time to put it
all together!!
10.2 Day 3 Systems of Linear Equations Matrices 2010
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December 08, 2010
Nov 3012:40 PM
Solve a System of Linear Equations Using Matrices
{2x + 2y = 6 x + y + z = 13x + 4y z = 13
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.
Step 2: Use row operations to change into row echelon form. HINT: Start with the first column.
Step 3: Solve for each variable.
x = 1, y = 2, z = 2Answer:
10.2 Day 3 Systems of Linear Equations Matrices 2010
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December 08, 2010
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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 = 02x + 4y 3z = 06x + 2y + z = 0
{
x = z, y = z, z = any real numberAnswer: 12
10.2 Day 3 Systems of Linear Equations Matrices 2010
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December 08, 2010
Nov 3012:40 PM
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 = 62x y z = 3 x + 2y + 2z = 0
InconsistentAnswer:
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Homework: page 754 (37 59 odd)
