For anyone who is already familiar with the Prof. Strang's lectures from previous years, the main new thing in this five-lecture mini-series is he tries to cond

For anyone who is already familiar with the Prof. Strang's lectures from previous years, the main new thing in this five-lecture mini-series is he tries to condense the material even further—maximum intuition and power-ideas, instead of the full-length in-class lecture format with derivations. This makes the material difficult to understand for beginners, but makes a great second source in addition to or after a regular LA class. One of the interesting new ways of thinking in these lectures is the A = CR decomposition for any matrix A, where C is a matrix that contains a basis for the column space of A, while R contains the non-zero rows in RREF(A) — in other words a basis for the row space, see https://ocw.mit.edu/resources/res-18-010-a-2020-vision-of-linear-algebra-spring-2020/videos/MITRES_18_010S20_LA_Slides.pdf#page=7 https://ocw.mit.edu/resources/res-18-010-a-2020-vision-of-li... Example you can play with: https://live.sympy.org/?evaluate=C%20%3D%20Matrix(%5B%5B1%2C4%5D%2C%20%5B3%2C2%5D%2C%20%5B2%2C1%5D%5D)%0A%23--%0AC%0A%23--%0AR%20%3D%20Matrix(%5B%5B1%2C0%2C1%5D%2C%20%5B0%2C1%2C1%5D%5D)%0A%23--%0AR%0A%23--%0AC*R%0A%23--%0A(C*R).rref()%5B0%5D%0A%23--%0A https://live.sympy.org/?evaluate=C%20%3D%20Matrix(%5B%5B1%2C... Thinking of A as CR might be a little intense as first-contact with linear algebra, but I think it contains the "essence" of what is going on, and could potentially set the stage for when these concepts are explained (normally much later in a linear algebra course). Also, I think the "A=CR picture" is a nice justification for where RREF(A) comes about... otherwise students always complain that the first few chapters on Gauss-Jordan elimination is "mind-numbing arithmetic" (which is kind of true...) but maybe if we present the algorithm as "finding the CR-decomposition which will help you understand dozens of other concepts in the remainder of the course" it would motivate more people to learn about RREFs and the G-J algo.