# Accelerated Algebra Holiday Review

## Matrix

A matrix is simply a group or array of numbers, symbols or expressions arranged in a certain way. In a matrix, these numbers or symbols are arranged in rows and columns enclosed in a somewhat box shape. They are often labeled by their dimensions such as the 3x3 Matrix above. Matrices can be deciphered in many ways and are very helpful in the world of mathematics. Some functions of Matrices include, adding, subtracting and multiplying matrices, solving for the determinate or inverse of matrices.

Adding and subtracting matrices is a simple process where all you need is basic addition addition and subtraction skills. You must know that matrices can only be added or subtracted if the dimensions are the same. So a 3x3 matrix can not be added with a 3x2 matrix. Once you have to matrices with the same dimensions you simply add or subtract the numbers inside a matrix with the numbers in the corresponding spot of the other matrix.

## Solving for Determinants and Inverses

A determinant is a quantity that shows a certain relationship between the numbers of a matrix. In a 2x2 matrix, the determinant is obtained by using the rule ad-bc in the matrix abdc. In a 3x3 matrix solving for the determinant gets a little more complicated. You must multiply a series of diagonals which are then subtracted from the multiplication of the opposite diagonals.

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

Multiplying matrices is a fairly simple process that requires basic skills. Matrices can only be multiplied if the two have the same inner dimension number. If not, the answer is undefined. In order to multiply matrices you must multiply each row of the first matrix by each column of the second matrix, which will determine each number in the final product.

## Applications of Matrices

Matrices are a very important concept which aid in several other processes both in and out of the math world.

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

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

## Citations

• Glencoe Algebra 2 Textbook