A matrix is a rectangular array of numbers or expressions laid out by rows and columns; treated as a single element and manipulated according to rules

the horizontal lines on the matrices are rows the vertical lines are columns.the numbers in the matrices are the elements.the dimesion of a matrix depends on how much element it has for example

the dimesion for this matrix is 2 by 3 because it has 2 rows and 3 columns.

You always count the rows first then the columns.

a row matrix is called a row vector it’s a matrix with one row of elements

a column matrix is a column vector it’s the same as row vector except

it has one column instead

of a row. A square matrix is a matrix with the same number of rows as columns

When you add matrices you add the numbers that are in the same row and

column for example

it’s the same for subtracting matrixes

when you multiply matrices together the columns of the first matrix needs to match the rows of the second one In the picture on the left, the matrices can be multiplied since the number of columns in  the 1st one, matrix A, equals the number of rows in the 2nd,

matrix B.

If it doesn’t have the same numbers of columns and rows than the two

matrices cannot be multiplied

Matrix C and D below cannot be multiplied together because the number of columns in C does not equal the number of rows in D. In this case, the multiplication of these two matrices is not defined. (http://www.mathwarehouse.com/algebra/matrix/multiply-matrix.php)

REAL WORLD APPLICATIONS:

Medicine: Five diabetic patients in a hospital each require injections of three kinds of insulin each day. The 5x3 matrix shown below gives the

amounts of the three kinds of insulin each patient requires each day. If patient 1 plans to stay 10 days, patient 2 stays 5 days, patient 3 stays 20 days, patient 4 stays 10 days, and patient 5 stays 15 days, how much of each type of insulin must the medical staff have on hand?

Patient 1 Patient 2 Patient 3 Patient 4 Patient 5

Semi-lente 10 units 40 units 30 units 20 units 10 units

lente 20 units 20 units 10 units 10 units 10 units

Ultra-insulin 30 units 5 units 5 units 20 units 10 units

http://www.mathme.com/henderson/mrhenderson/algebra2/worksheets/matrixwordproblems.htm

Matrices can be used in everyday life in medicine,restaurants, contruction, and even traveling they can help to see how much medicine

they might need or how much food they’ve sold even to see how many people traveling. Matrices can be used in everyday life in hospitals,restaurants, and factories.