MATH 221: Applied Linear Algebra
James Cook's Applied Linear Algebra Homepage:


Useful Materials and Links:
  1. Course Planner includes dates for Tests etc...
  2. Applied Linear Algebra Lecture Notes
  3. Matrix Theory and Linear Algebra (free book website, this is the required text for course we use on occasion)
  4. Applied Linear Algebra (Math 221-003) of Fall 2025
    Playlist on You Tube:
  5. Matrix Calculator Site - Will show steps for rref and many other calculations.
  6. Eigenvector calculator, ugly numbers no problem. Also deals with complex case no problem. However, does not find generalized e-vectors.
  7. Note on why the CCP is true and how to reverse engineer a matrix with it (for this video)
  8. Note on definition of matrix w.r.t. basis for linear transformation on Rn (for this video)
  9. Applied Linear Algebra (Math 221-001) of Spring 2025
    Playlist on You Tube:
Practice Missions:
I originally offered these as homework for Math 221 in the Spring 2025 term. Now I am using them as practice problems for future semesters. They still earn points, but now I provide solutions from the outset. You get the most out of these by working them and then checking them. However, no need to be stuck for too long since the solutions are given below:
Old Tests and Quiz Solutions:

Additional Examples:
Solutions to Homework from a previous year:
  1. Homework 1: on linear systems and Gaussian Elimination
  2. Homework 2: matrix properties, elementary and inverse matrices
  3. Homework 3: calculating inverse matrix, and determinants, Kramer's Rule
  4. Homework 4: spanning sets, linear independence, CCP, coordinate vectors
  5. Homework 5: row, column and null space of a matrix
  6. Homework 6: linear transformations
  7. Homework 7: dot-products, Gram Schmidt, orthogonal complements
  8. Homework 8: orthogonal operators and least square fitting
  9. Homework 9: inner products, real e-values and e-vectors
  10. Homework 10: e-value theory and complex e-values and vectors
  11. Homework 11: diagonalization and eigenbases
  12. Homework 12: solving systems of ODEqns via the matrix exponential/e-vector method
Solutions from my 2012 version of Math 221, based somewhat on Anton
  1. Homework 1:
  2. Homework 2:
  3. Homework 3:
  4. Homework 4:
  5. Homework 5:
  6. Homework 6:
  7. Homework 7:
  8. Homework 8:
  9. Homework 9:
  10. Homework 10:
Solutions from my 2017 version of Math 221, based somewhat on Shore
  1. Homework 1:
  2. Homework 2:
  3. Homework 3:
Select examples on various problems
  1. Overview of Row Reduction including LU and PLU decomposition and the CCP (written by my brother William Cook of Appalachian State University)
  2. Chemical Balancing Example from a textbook
  3. a 4x7 rref example via the web calculator
  4. large rref example via the web calculator
  5. calculate rref of 4x4 example via the web calculator
  6. calculate inverse of 4x4 example via the web calculator
  7. Gram-Schmidt Algorithm example
I gave computer projects in Spring 2024, but I've decided to move the computer work to other places in future.
Computer Projects:
  1. Computer Project A orthonormalization, construction of matrix with particular set of eigenvalues and vectors, applications.
  2. Computer Project B random matrix generation, orthonormalization, finding spectrum and diagonalizing, applications.
  3. Computer Project C orthonormalization, construction of matrix with particular Jordan form, applications.
  • 2024 Applied Linear Algebra Lecture Notes (last used in in Spring 2025 class)


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    Last Modified: 8-11-2025