Technically, though, we don't know if this function is continuous or if it is defined by that table and only has those 5 points.

A quadratic describes the points that make a parabola. So, in each case shown in the table, y = x² + 10 and that is definitely a quadratic. In §7.5, he attempts to address the confusion this caused one student who complained, but I would think it better to bother to use set-builder notation and thus to avoid the problem altogether, as do three of the four freely-available linear algebra textbooks recommended by the American Institute of Mathematics (the one that doesn’t omits null spaces entirely).ĭr Grinfeld, and perhaps his students, likely would make fewer mistakes in Gaussian elimination were he to use augmented matrix notation, as is used in the said three textbooks.In Sal's table, notice that every value of y equals 10 plus x^2

§2.12, “Linear Subspaces of the Plane”, is confusing enough that I think it ought to be redone - for now, read the comment under the video.ĭr Grinfeld habitually abuses notation for null spaces, writing a linear combination with unknown coefficients to represent the set of all linear coefficients of its form.

I think Dr Grinfeld's linear algebra material is certainly good for its price ($0.00), although my notes from going through the first eight or so chapters note the following small number of issues: There is a website named Lemma run by one Pavel Grinfeld that has a course in linear algebra that is similar to Khan Academy's more developed material, in that it has short lecture videos interspersed with exercises that are graded automatically by the website.

Khan academy algebra linear