Learn Intro to matrix inverses Finding inverses of 2x2 matrices Determinant of a 2x2 matrix Determining invertible matrices Solving linear systems with matrices Representing linear …

What I want to do in this video is explore the notion of a matrix outside of the context of a surprisingly good movie that involves Keanu Reeves. And it's actually the first of three.

Determinants originate as applications of vector geometry: the determinate of a 2x2 matrix is the area of a parallelogram with line one and line two being the vectors of its lower left hand sides.

This right here, by definition, this is the matrix A times the matrix B. The definition of matrix products is you take the first matrix and multiply times the column vectors of the second matrix.

Sal defines what it means to add or subtract matrices. He shows a few examples and discusses some important properties of matrix addition and subtraction.

So you're not just blindly doing some-- matrix-matrix products can be pretty tedious, but now you know what they're for. They're actually for the composition of two transformations where each …

A number, plain and simple. A number that is a matrix or a vector, just a number, that is a scalar.

But if matrix A is not a square matrix, then these are going to be two different identity matrices, depending on the appropriate dimensions. Now, let's see if we can extend this analogy …

In eukaryotes, the citric acid cycle takes place in the matrix of the mitochondria, just like the conversion of pyruvate to acetyl CoA . In prokaryotes, these steps both take place in the …

This topic covers: - Adding & subtracting matrices - Multiplying matrices by scalars - Multiplying matrices - Representing & solving linear systems with matrices - Matrix inverses - Matrix …