Linear Algebra

Kevin Hopkins, Oct 21, 2014

Worksheets that go along with a Linear Algebra Course

Table of Contents

  1. Exam One Material
    1. Where might systems come from?
    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
  2. Exam Two Material
    1. Visualize Span
    2. Is a vector in the Span?
    3. Testing for Independent Column Vectors
    4. Independent Set from Dependent Set
    5. Matrix Operations of +, -, and *
    6. Operations on ONE matrix
    7. Operations on ONE matrix, that is not square.
    8. Row Space
    9. Spaces Associated with a Matrix
  3. Exam Three Material
    1. Eigenvalue/Eigenvector
    2. Eigenvalue/Eigenvector-A second Attempt
  4. Exam Four Material
  5. Tools for Use in ALL Exams
    1. Row Reducing a Matrix

1.

Exam One Material

[color=#c51414][b]Exam one will be over solving systems of equations through Linear Combinations[/b][/color]

  • 1. Where might systems come from?
  • 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

1.1.

Where might systems come from?

How do written problems become modeled by systems of equations?
– Kevin Hopkins

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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2.

Exam Two Material

[color=#c51414][b]Exam two will be over Spanning sets through row and column spaces.[/b][/color]

  • 1. Visualize Span
  • 2. Is a vector in the Span?
  • 3. Testing for Independent Column Vectors
  • 4. Independent Set from Dependent Set
  • 5. Matrix Operations of +, -, and *
  • 6. Operations on ONE matrix
  • 7. Operations on ONE matrix, that is not square.
  • 8. Row Space
  • 9. Spaces Associated with a Matrix

2.1.

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
– Kevin Hopkins

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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3.

Exam Three Material

[color=#c51414][b]Exam Three will be over Vector Spaces through Eigenvalues.[/b][/color]

  • 1. Eigenvalue/Eigenvector
  • 2. Eigenvalue/Eigenvector-A second Attempt

3.1.

Eigenvalue/Eigenvector

Finding eigenvalue and eigenvector for a 2 by 2 matrix. With an option to visualize the transformation.
Eigenvalue/Eigenvector
– Kevin Hopkins

3.2.

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4.

Exam Four Material

[color=#c51414][b]Exam Four will be over Linear Transformations and Representations.[/b][/color]


    This chapter does not contain any resources yet.

5.

Tools for Use in ALL Exams

[color=#c51414][b]Tools for use in all exams.[/b][/color]

  • 1. Row Reducing a Matrix

5.1.

Row Reducing a Matrix

[color=#b20ea8][b]Select the size of matrix you want.[br]Enter the matrix elements in the Spreadsheet at the bottom.[br]Matrix should show up on screen.[br]Once entered completely, you should see the reduced row echelon form of that matrix.[br]Depending on the problem, this reduced matrix will be interpreted in a variety of ways.[br]You do need to know how to row reduce by hand, but some problems can be done with the computer.[/b][/color][br][br][b][color=#c51414]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.[/color][/b]
Row Reducing a Matrix
– Kevin Hopkins

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