 # A 2021 Vision of Linear Algebra: Become an Algebra Master

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These six 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 AlgebraOrthogonal VectorsEigenvalues & Eigenvectors; and Singular Values & Singular Vectors. Singular values have become so important and they come directly from the eigenvalues of A’A.

### What Will You Learn?

• Operations, including order of operations (PEMDAS) and like-terms
• Equations and systems of equations, including inverse operations, direct and inverse variation, and distance/rate/time problems
• Graphing, including parallel and perpendicular lines, and parabolas
• Polynomials and factoring, including the quadratic formula and completing the square
• Functions, including domain and range, and sums and products of functions
• Inequalities, including trichotomy and graphing inequalities and conjunctions on a number line
• Exponential and logarithmic functions, including laws of logs, change of base, and graphing

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