# Accelerated Algebra Holiday Review

### By: Ben Scire

## Matrix

## Adding and Subtracting Matrices

## Solving for Determinants and Inverses

The inverse of a matrix represents the same inverse as shown with integers. It is simply the matrix to the -1st power. With the basic integer 2, the inverse is 1/2, but with matrices solving for the inverse is more complicated. With the matrix abcd to solve for the inverse you must multiply the inverse of the determinant by the matrix rearranged into matrix d(-b)(-c)a.

## Multiplying Matrices

## Applications of Matrices

Within the math world matrices can be used as a form of organizing data. Most commonly, matrices are used to help solve a system of equations by using a formula which involves inverses and multiplication. When dealing with a system of three equations with three unknowns matrices prove to be very helpful in solving for the variables. By plugging coefficients into the matrix and completing the formula, matrices give a much easier method of solving these unknowns.

Outside of the math world, matrices have many very important functions that are not seen to the average person. Matrices are applied in several branches of science, mainly within computer software as a form of organizing data. The use of matrices within a computer helps us calculate electrical properties of a circuit, through voltage, amperage, and resistance. This helps with transformations of images and specific computer graphics.

Matrix mathematics is very helpful because it is a form of simplifying linear algebra. It provides a more compact way to deal with equations, variables and expressions, resulting in the various functions it has today.

## Concept Summary

- Matrix is an array of numbers, symbols, or expressions that can be used for multiple functions.
- In order to add or subtract matrices simply add or subtract corresponding numbers. (Must be same dimensions)
- WHen determining the inverse or determinant of a matrix follow formulas for each.
- To multiply matrices multiply the rows of the first by the columns of the second

## Coming up Next

- Quiz 4 on Monday, December 7th
- Test 2 on Thursday, December 10th

## Citations

- Glencoe Algebra 2 Textbook
- Google Images