# Digital Audiovisual Lectures

Chapter 01: Introduction [MORE]

Chapter 02: Vectors [MORE]

• Prove that if a set of vectors contains a null vector, the set of vectors is linearly dependent [YOUTUBE 2:29] [TRANSCRIPT]
• Prove that if a set of vectors is linearly independent, then a subset of it is also linearly independent [YOUTUBE 5:42][TRANSCRIPT]
• Prove that if a set of vectors is linearly dependent, then at least one vector can be written as a linear combination of others [YOUTUBE 4:06] [TRANSCRIPT]
• How can vectors be used to write simultaneous linear equations? [YOUTUBE 5:08] [TRANSCRIPT]
• How can vectors be used to write simultaneous linear equations? Example [YOUTUBE 3:13][TRANSCRIPT]

Chapter 03: Binary Matrix Operations [MORE]

Chapter 04: Unary Matrix Operations [MORE]

Chapter 05: System of Equations [MORE]

• A real life problem of setting up simultaneous linear equations [YOUTUBE 5:23] [TRANSCRIPT]
• Writing simultaneous linear equations in matrix form [YOUTUBE 5:25] [TRANSCRIPT]
• Distinguishing between consistent and inconsistent system of equations based on rank of matrices [YOUTUBE 3:06] [TRANSCRIPT]
• Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 1 [YOUTUBE 4:15] [TRANSCRIPT]
• Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 2 [YOUTUBE 8:42] [TRANSCRIPT]
• Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 3 [YOUTUBE 6:07] [TRANSCRIPT]
• If a solution exists, how do we know if it is unique? [YOUTUBE 3:25] [TRANSCRIPT]
• Does a set of equations have a unique solution? Example 1 [YOUTUBE 2:18] [TRANSCRIPT]
• Does a set of equations have a unique solution? Example 2 [YOUTUBE 2:23] [TRANSCRIPT]
• If we have more equations than unknowns, does it mean we have inconsistent system of equations? [YOUTUBE 8:11] [TRANSCRIPT]
• Can a system of equations have more then one but not infinite number of solutions? [YOUTUBE 4:57] [TRANSCRIPT]

Chapter 06: Gaussian Elimination [MORE]

• Naive Gaussian elimination: Theory: Part 1 of 2 [YOUTUBE 10:27] [TRANSCRIPT]
• Naive Gaussian elimination: Theory: Part 2 of 2 [YOUTUBE 2:22] [TRANSCRIPT]
• Naive Gauss Elimination Method: Example: Part 1 of 2 (Forward Elimination) [YOUTUBE 10:49] [TRANSCRIPT]
• Naive Gauss Elimination Method: Example: Part 2 of 2 (Back Substitution) [YOUTUBE 6:40] [TRANSCRIPT]
• Pitfalls of Naive Gauss Elimination Method: [YOUTUBE 7:20] [TRANSCRIPT]
• Naive Gauss Elimination: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 7:20] [TRANSCRIPT]
• Naive Gauss Elimination: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 7:40] [TRANSCRIPT]
• Naive Gauss Elimination: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 8:07] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Theory [YOUTUBE 10:39] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Example: Part 1 of 3 (Forward Elimination) [YOUTUBE 7:15] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Example: Part 2 of 3 (Forward Elimination) [YOUTUBE 10:08] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Example: Part 3 of 3 (Back Substitution) [YOUTUBE 6:18] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 8:58] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 8:17] [TRANSCRIPT]
• Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 5:48] [TRANSCRIPT]
• Determinant of a Matrix Using Forward Elimination Method: Background [YOUTUBE 5:17] [TRANSCRIPT]
• Determinant of a Matrix Using Forward Elimination Method: Example [YOUTUBE 10:07] [TRANSCRIPT]

Chapter 07: LU Decomposition [MORE]

Chapter 08: Gauss-Seidel Method [MORE]

• Gauss-Seidel Method of Solving Simul Linear Eqns: Theory: Part 1 of 2 [YOUTUBE 8:01] [TRANSCRIPT]
• Gauss-Seidel Method of Solving Simul Linear Eqns: Theory: Part 2 of 2 [YOUTUBE 5:38] [TRANSCRIPT]
• Gauss-Seidel Method of Solving Simul Linear Eqns: Example: Part 1 of 2 [YOUTUBE 9:17] [TRANSCRIPT]
• Gauss-Seidel Method of Solving Simul Linear Eqns: Example: Part 2 of 2 [YOUTUBE 7:40] [TRANSCRIPT]
• Gauss-Seidel Method of Solving Simul Linear Eqns:
• Gauss-Seidel Method of Solving Simul Linear Eqns:

Chapter 09: Adequacy of Solutions [MORE]

• ill-conditioned and well-conditioned system of equations [YOUTUBE 10:12] [TRANSCRIPT]
• Relating changes in coefficient matrix to changes in solution vector [YOUTUBE 4:18] [TRANSCRIPT]
• Relating changes in coefficient matrix to changes in solution vector Proof [YOUTUBE 8:46] [TRANSCRIPT]
• Relating changes in right hand side vector to changes in solution vector [YOUTUBE 3:12] [TRANSCRIPT]
• Number of significant digits correct in my solution vector Theory [YOUTUBE 4:00] [TRANSCRIPT]
• Number of significant digits correct in my solution vector Example 1 [YOUTUBE 3:57] [TRANSCRIPT]
• Number of significant digits correct in my solution vector Example 2 [YOUTUBE 4:26] [TRANSCRIPT]

Chapter 10: Eigenvalues and Eigenvectors [MORE]

• A physical example of application of eigenvalues and eigenvectors [YOUTUBE 16:23] [TRANSCRIPT]
• How does one find eigenvalues and eigenvectors numerically [YOUTUBE 4:57] [TRANSCRIPT]
• How does one find eigenvalues and eigenvectors numerically Example [YOUTUBE 8:09][TRANSCRIPT]