# A 2020 Vision of Linear Algebra | Supplemental Resources | MIT OpenCourseWare

### Description

These brief videos, recorded in 2020, contain ideas and suggestions from Professor Strang about the recommended order of topics in teaching and learning linear algebra. The first topic is called _A New Way to Start Linear Algebra_. The key point is to start right in with the columns of a matrix _A_ and the multiplication _Ax_ that combines those columns.
That leads to _The Column Space of a Matrix_ and the idea of independent columns and the factorization _A = CR_ that tells so much about _A_. With good numbers, every student can see dependent columns.
The remaining videos outline very briefly the full course: _The Big Picture of Linear Algebra_; _Orthogonal Vectors_; _Eigenvalues & Eigenvectors_; and _Singular Values & Singular Vectors_. Singular values have become so important and they come directly from the eigenvalues of _A’A_.
A new video recorded in 2021, _Finding the Nullspace: Solving Ax = 0 by Elimination_, computes the nullspace of any matrix _A_.
You can see this new idea developing in the [first video lecture](/courses/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/resources/lecture-1-the-column-space-of-a-contains-all-vectors-ax) of Professor Strang’s 2019 course _[18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning](/courses/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/)_.

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