Linear combinations, length and the dot product, matrix times vector by rows and by columns, and the column space. 5 short slides, then worked examples and problems. Each slide has an everyday picture, a worked example and Python you can run right on the page.
Lesson 1Linear combinationsLinear combinations: stretch vectors, then add themOpen slide →01 · Strang §1.1 · Linear combinationsWhat cv + dw really means, with an everyday picture, a worked example and Python you can run in your browser. Follows Strang §1.1.
Lesson 1Dot productLength and the dot productOpen slide →02 · Strang §1.2 · Lengths and dot productsWhat the dot product v · w means, how to compute it, how the length of a vector comes from it, and why a zero dot product means a right angle. Python in your browser. Strang §1.2.
Lesson 1Matrix times vectorMultiplying a matrix by a vectorOpen slide →03 · Strang §1.3 · MatricesWhy Ax is a mix of the columns of A, explained with a shopping basket, a worked example and live Python. Row way vs column way. Strang §1.3.
Lesson 1Column spaceThe column space: every place Ax can reachOpen slide →04 · Strang §1.3 and §3.1 · Column spaceThe column space is everything Ax can reach. Learn it with a simple walking picture, rank, a worked example and Python you can run. Strang §1.3 and §3.1.
Lesson 1RecapWhat you can now do.Open slide →05 · Recap · ReadingThe core ideas of Strang chapter 1 on one page: linear combinations, length and dot product, Ax by rows and by columns, and the column space.
