# MATRIX ALGEBRA

May 29th, 2015
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1. WHAT IS A MATRIX? A matrix is defined as rectangular array of numbers, parameters, or variables.Matrix algebra provides a method to solve a system of simultaneous equations: 1. It provides a compact way of writing an equation

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MATRIX ALGEBRA1. WHAT IS A MATRIX?A matrix is defined as rectangular array of numbers, parameters, or variables.Matrix algebra provides a method to solve a system of simultaneous equations:1. It provides a compact way of writing an equation system.2. It provides a procedure to test for the existence of a solution.3. If the solution exists, it provides a method of finding that solution.General format of a system of m equations with n variables:a11x1 + a12x2 + ??? + a1nxn = d1a21x1 + a22x2 + ??? + a2nxn = d2??????????????????????????????????????????am1x1 + am2x2 + ??? + amnxn = dmThe matrix format of writing a system of equations is as follows.The shorthand way of representing matrix A is: A = [aij]Example 1:6x1 + 3x2 + x3 = 22x1 + 4x2 ? 2x3 = 124x1 ? x2 + 5x3 = 10In matrix format the equation is presented as:The number of rows and number of columns of a matrix define the dimension of the matrix. The dimension is shown as m n. A matrix with 4 rows and 3 columns is a "4 by 3" matrix: 4 3.A matrix with m rows and 1 column is called a column vector: m 1. Similarly, a matrix with 1 row and n columns is called a row vector: 1 n.A system of simultaneous equations can be represented as:Ax = dThe shorthand representation of the system of equations implies that the left-hand side of the equation is obtained as the product of the coefficient matrix A times the variable matrix x. The product of these two matrices produces a new

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