Inverse of 4x4 Matrix Using Adjugate Formula 
Inverse of 4x4 Matrix Using Adjugate Formula
by Robert Donley
Video Lecture 11 of 47
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Views: 50,012
Date Added: March 15, 2015

Lecture Description

Linear Algebra: We find the inverse of a 4x4 matrix using the adjugate (or classical adjoint) formula. Key steps include computing minors and the trick for 3x3 determinants.

Course Index

  1. Row Reduction for a System of Two Linear Equations
  2. Solving a 2x2 SLE Using a Matrix Inverse
  3. Solving a SLE in 3 Variables with Row Operations 1
  4. Solving a SLE in 3 Variables with Row Operations 2
  5. Consistency of a System of Linear Equations
  6. Inverse of 3 x 3 Matrix Using Row Operations 1
  7. Inverse of 3x3 Matrix Using Row Operations 2
  8. Inverse of 4x4 Matrix Using Row Operations
  9. Example of Determinant Using Row Echelon Form
  10. Inverse of 3 x 3 Matrix Using Adjugate Formula
  11. Inverse of 4x4 Matrix Using Adjugate Formula
  12. Cramer's Rule for Three Linear Equations
  13. Determinant of a 4 x 4 Matrix Using Cofactors
  14. Determinant of a 4 x 4 Matrix Using Row Operations
  15. Examples of Linear Maps
  16. Example of Linear Combination
  17. Example of Linear Combination (Visual)
  18. Evaluating Linear Transformations Using a Basis
  19. Linear Transformations on R^2
  20. Example of Checking for Basis Property
  21. Example of Basis for a Null Space
  22. Example of Basis for a Span
  23. Example of Linear Independence Using Determinant
  24. Example of Kernel and Range of Linear Transformation
  25. Linear Transformations: One-One
  26. Linear Transformations: Onto
  27. Example of Change of Basis
  28. Eigenvalues and Eigenvectors
  29. Example of Eigenvector: Markov Chain
  30. Example of Diagonalizing a 2 x 2 Matrix
  31. Example of Power Formula for a Matrix
  32. The Fibonacci Numbers Using Linear Algebra (HD Version)
  33. Vector Length in R^n
  34. The Standard Inner Product on R^n
  35. Example of Fourier's Trick
  36. Example of Orthogonal Complement
  37. Orthogonal Transformations 1: 2x2 Case
  38. Orthogonal Transformations 2: 3x3 Case
  39. Example of Gram-Schmidt Orthogonalization
  40. QR-Decomposition for a 2x2 Matrix
  41. Beyond Eigenspaces: Real Invariant Planes
  42. Beyond Eigenspaces 2: Complex Form
  43. Spectral Theorem for Real Matrices: General 2x2 Case
  44. Spectral Theorem for Real Matrices: General nxn Case
  45. Example of Spectral Theorem (3x3 Symmetric Matrix)
  46. Example of Spectral Decomposition
  47. Example of Diagonalizing a Symmetric Matrix (Spectral Theorem)

Course Description

This course contains 47 short video lectures by Dr. Bob on basic and advanced concepts from Linear Algebra. He walks you through basic ideas such as how to solve systems of linear equations using row echelon form, row reduction, Gaussian-Jordan elimination, and solving systems of 2 or more equations using determinants, Cramer's rule, and more.

He also looks over concepts of vector spaces such as span, linear maps, linear combinations, linear transformations, basis of a vector, null space, changes of basis, as well as finding eigenvalues and eigenvectors.

Finally, he finishes the course covering some advanced concepts involving eigenvectors, including the diagonalization of the matrix, the power formula for a matrix, solving Fibonacci numbers using linear algebra, inner product on R^n, orthogonal transformations, Gram-Schmidt orthogonalization, QR-decomposition, the spectral theorem, and much more.

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