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# MATH 1630 If high school precalculus and ACT math of at least 21 contact 694 MATH 1630

pellissippi state community college

GPA 3.92

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This 0 page Class Notes was uploaded by Brown Lowe on Sunday November 1, 2015. The Class Notes belongs to MATH 1630 at pellissippi state community college taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/232969/math-1630-pellissippi-state-community-college in Mathematics (M) at pellissippi state community college.

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Date Created: 11/01/15

MATRIX ARITHMETIC Addition and Subtraction of Matrices 1 A matrix of order m x n has m rows and n columns row x column a In a square matrix m n b In a row matrix m 1 c In a column matrix n 1 2 Two matrices are equal if they have the same order and each pair of corresponding elements is equaL a Giventhat 9 7 mis 5 r 0 8 0 b Then 9m3m12 7 n 5 n 2 r 8 3 To addsubtract two matrices of the same order addsubtract the corresponding elements You cannot add or subtract matrices if they are not the same size 4 The additive inverse negative of matrix X is formed by changing each element to its opposite and is denoted by X 5 The additive identity zero matrix has zeros for all elements The zero matrix is not unique their is one to match a matrix of any size 6 Examples Given that A 4 73 0 5 and B 1 74 72 6 71 0 3 7 1 8 73 5 A B 5 77 72 1 1 0 8 0 12 The0matrixoforder2x4is0 0 0 0 l Z l ll 3H 1H Zl Matrix Arithmetic page 1 J Ahrens 192006 A N 9 A l Scalar Multiplication A scalar is a real number not a matrix To multiply a scalar times a matrix multiply each element of the matrix by the scalar quotA 47305then3A3 47305 12 79015 71037 71037 730921 IfB174 72 6 then3A4B 12 79 o 15 4174 72 6 18735 73 0921 18735 12 79 o 15 4 716 is 24 73 o 9 21 4 32 712 2o 8 7 8 79 77 732 21 1 Matrix Multiplication True matrix multiplication can be very tricky a It is not always possible to multiple two given matrices even if they are the same size b It may be possible to multiply A times B in that order but not B times A c It may be possible to multiply A times B and B times A but not get the same answer The sizes of the matrices will determine whether or not they can be multiplied a Suppose that we have matrix A which is 3x2 and matrix B which is 2x3 b Write the orders of the matrices sidebyside and compare the two inner numbers c If the number of columns in the first matrix is equal to the number of rows in the second matrix then the product AB can be found d Ifthe product exists then its size is given by the two outer numbers matrix A matrixB 2 x 3 3 T f T must be AB will be 3 x 3 e Would we be able to find BA in this case Yes it will be a 2x2 matrix matrix B matrixA 3 x 2 T f T must be BA will be 2 x 2 Matrices form a mathematical system of their own so they do not have to follow the same rules that the real numbers do Matrix Arithmetic page 2 J Ahrens 192006

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