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Linear Algebra
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1. Exam One Material
- Where might systems come from?
- Solving a system of equations-Section 3.1-3.2 in College Alg
- Solving a system of equations: 3 by 3
- Solving a system of equations where there may not be one sln
- Solving a homogeneous system of equations
- Find Linear Combinations
- Finding Coefficients for a Linear Combination
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2. Exam Two Material
- Visualize Span
- Is a vector in the Span?
- Testing for Independent Column Vectors
- Independent Set from Dependent Set
- Matrix Operations of +, -, and *
- Operations on ONE matrix
- Operations on ONE matrix, that is not square.
- Row Space
- Spaces Associated with a Matrix
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3. Exam Three Material
- Eigenvalue/Eigenvector
- Eigenvalue/Eigenvector-A second Attempt
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4. Exam Four Material
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5. Tools for Use in ALL Exams
- Row Reducing a Matrix
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Linear Algebra
Kevin Hopkins, Oct 21, 2014
Worksheets that go along with a Linear Algebra Course
Table of Contents
- Exam One Material
- Where might systems come from?
- Solving a system of equations-Section 3.1-3.2 in College Alg
- Solving a system of equations: 3 by 3
- Solving a system of equations where there may not be one sln
- Solving a homogeneous system of equations
- Find Linear Combinations
- Finding Coefficients for a Linear Combination
- Exam Two Material
- Visualize Span
- Is a vector in the Span?
- Testing for Independent Column Vectors
- Independent Set from Dependent Set
- Matrix Operations of +, -, and *
- Operations on ONE matrix
- Operations on ONE matrix, that is not square.
- Row Space
- Spaces Associated with a Matrix
- Exam Three Material
- Eigenvalue/Eigenvector
- Eigenvalue/Eigenvector-A second Attempt
- Exam Four Material
- Tools for Use in ALL Exams
- Row Reducing a Matrix
Exam One Material
Exam one will be over solving systems of equations through Linear Combinations
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1. Where might systems come from?
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2. Solving a system of equations-Section 3.1-3.2 in College Alg
-
3. Solving a system of equations: 3 by 3
-
4. Solving a system of equations where there may not be one sln
-
5. Solving a homogeneous system of equations
-
6. Find Linear Combinations
-
7. Finding Coefficients for a Linear Combination
Where might systems come from?
How do written problems become modeled by systems of equations?
Exam Two Material
Exam two will be over Spanning sets through row and column spaces.
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1. Visualize Span
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2. Is a vector in the Span?
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3. Testing for Independent Column Vectors
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4. Independent Set from Dependent Set
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5. Matrix Operations of +, -, and *
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6. Operations on ONE matrix
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7. Operations on ONE matrix, that is not square.
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8. Row Space
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9. Spaces Associated with a Matrix
Visualize Span
Visualize linear combinations of 1, 2, or 3 vectors in the plane to begin to see what the span of a set may look like.
Visualize Span
Eigenvalue/Eigenvector
Finding eigenvalue and eigenvector for a 2 by 2 matrix. With an option to visualize the transformation.
Eigenvalue/Eigenvector
Row Reducing a Matrix
Select the size of matrix you want.
Enter the matrix elements in the Spreadsheet at the bottom.
Matrix should show up on screen.
Once entered completely, you should see the reduced row echelon form of that matrix.
Depending on the problem, this reduced matrix will be interpreted in a variety of ways.
You do need to know how to row reduce by hand, but some problems can be done with the computer.
Don't remove any of the ?, simply replace them. Removing any ? messes up the entire process with this file. You will need to reload the entire page.
Row Reducing a Matrix
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