01Introductions to Matrices

# 01Introductions to Matrices - INTRODUCTION TO MATRICES...

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I NTRODUCTION TO M ATRICES Linear algebra is the art of solving systems of linear equations. For smaller systems, we have used substitution, elimination, and graphing. For larger systems it is necessary to use more systematic methods. To solve larger systems of linear equations we use matrices (we used this a little to solve systems of three linear equations on the GDC). Ex . You are given a set of three linear equations in three variables to solve. 1 10 4 5 5 2 2 4 8 2 = - + = + + = + + z y x z y x z y x To solve this system, a computer needs only the coefficients of the variables and the constant terms. - 1 1 10 4 5 1 5 2 2 4 8 2 This array of numbers is called a matrix . The matrix has 3 rows and 4 columns so it is called a 3 x 4 matrix. This is referred to as the order of the matrix and is given as n m × where m is the number of rows and n is the number of columns. . The first column of the matrix corresponds to the first variable,

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01Introductions to Matrices - INTRODUCTION TO MATRICES...

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