
Linear equations (Cramer's rule)
An independent system of three linear equations in three variables can be solved by using determinants and Cramer's rule. In this case we choose to expand by minors about the first column of the matrix.

Dimensional Analysis
Dimensional analysis is the analysis of the relationships between different physical quantities by identifying their fundamental dimensions.

Linear Equations (GaussJordan)
The solution to a system of equations in three variables is the set of all ordered triples that satisfy all of the equations of the system.

Multiplying radicals
In this case we are using binomial expansion to multiply radicals.

Quotient of Complex Numbers
We use complex conjugates to divide complex numbers. The process is the same as rationalizing the denominator.

Quadratic Equation
The following is an equation quadratic in form. Note that the term 2x  1 is repeated in the equation. Let A = 2x  1 and substitute A for 2x 1 in the equation.

Methods for solving quadratics
You have now learned to solve quadratic equations by four different methods: the evenroot property, factoring, completing the square, and the quadratic formula.

Functions Transformations
A function transformation takes the basic function f(x) and then "transforms" it or "translates" it.

Compositions of Functions
A composition of functions is the process of applying one function to another function. The symbol of composition of functions is a small circle between the function names.

Inverse functions
If an invertible function is defined by a formula, then the inverse function must reverse or undo what the function does.

Graphing Inverse functions
If a point (a,b) is on the graph of the function f, then (b,a) must be on the graph of its inverse.

Logarithmic functions
The properties of logarithms are very similar to the properties of exponents. In this case, we use the rules of logarithms to write the logarithm of a complicated expression in terms of logarithms of simpler expressions.