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Algebra II
Matrices
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Basics
As always, there you are with two equations staring you dead in the face. For example:x + 4y = 6 and2x + 3y = 9Remember that variables are the letters, and coefficients are just the numbers in fron...
Beginning Operations
First, we'll learn how to make a coefficient matrix. We'll start with the following examples:x + 4y = 6 2x – 3y = 9 This is all fine and dandy, we know all about coefficients. The first e...
Cramer's Rule
Cramer's Rule has nothing to do with Seinfeld, guitars, or horrible movie divorces. No, this has everything to do with solving square systems using our uptight friends, determinants. This is how Cr...
Cramer's Rule Redux
Determinants and Cramer's Rule Redux: Because Things Happen in ThreesHere is the first trick for using Cramer's Rule on 3 × 3 matrices. This does not work for 4 × 4s or larger matrices, and of co...
Adding and Subtracting Matrices
Adding, Subtracting, and Matrices, Oh My!It's simple to add and subtract matrices, but they must always be the same size for it to work. The answers are always the same size too. Check it out:All y...
Scalar Multiplication
Scalar Multiplication: One is the Loneliest Scalar?Multiply matrices by scalars to produce new matrices, for example, when all of the payoffs in a game are doubled.We know what you're thinking. Wha...
Multiplying Matrices
Multiplying Matrices: Further Down the Rabbit HoleThus far we've been dealing with operations that were reasonably simple; adding and subtracting matrices is limited to samesized matrices and scal...
In the Real World
Let's say you're working at A & F. You're in charge of shirts, because your manager thinks you have real promise. Don't let her down!First, you're doing inventory of red polo shirts. There are...
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