Module 6 Matrices & Applications Chapter 26 Matrices and Applications I

26.1 What is a Matrix?   A matrix (plural matrices) is a rectangular array of numbers arranged in rows and columns.   The numbers in a matrix are called the elements of the matrix.

Matrix representation   The ORDER of a matrix = number of rows x number of columns   E.g. The matrix shown below has 3 rows and 2 columns. We say that   it is a 3 by 2 rectangular matrix and its order is 3 by 2 (3 x 2).

  Capital letters will be used to represent matrices.   In general, a matrix with m rows and n columns is known as an m x n matrix. The elements in a matrix are referred to by the row and then by the column position.   The element in the second row and the first column of matrix A is -1. This is represented as a 21 = -1

Row matrices   A matrix with one row is called a row matrix or row vector.

Column Matrices   A matrix with one column is called a column matrix or column vector

Square Matrices   A matrix with an equal number of rows and columns is called a square matrix

Matrix Notation  The location of each element in the matrix is specified by its row and column number.

Example   A is a 1x 3 row matrix. The number 3 is represented by a 13.   B is a 3x3 diagonal matrix. The element in the 2, 1 position is 0 and the number 3 is represented by b 33.   C is a 3x 1 column matrix. The element in the 2, 1 position is 1 and the number 3 is represented by c 11.   D is a 2. 4 matrix. The element in the 2, 1 position is 2 and the number 3 is represented by d 23.   E is not a matrix.

Entering a matrix into a graphics calculator  Refer to pages 695 & 696 of your text book for notes on how to enter a matrix on the Ti-Nspire CAS.