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DIT4108 Applied Mathematics forScience and TechnologySession 4Basic operations of matricesTony Kwan
AgendaIntroductionProperties of MatricesTypes of MatricesAddition and SubtractionMultiplicationScalar MultiplicationMatrix Multiplication
IntroductionWhat is Matrix?
IntroductionWhy do we use it?
IntroductionDefinitionsA matrix is an array of numbersA=Denoted with aboldCapital letterAll matrices have an order (or dimension): Thenumber of rowsthe number of columns.Ais 2 by 3 or (23).5232221131211aaaaaa
IntroductionMatrix algebra has at least two advantages:Reduces complicated systems of equations to simpleexpressionsAdaptable to systematic method of mathematicaltreatment and well suited to computersDefinition:A matrix is a set or group of numbers arranged in a square or rectangulararray enclosed by two brackets110324dcba
PROPERTIES OF MATRICES7
Properties of MatricesA specified number of rows and a specifiednumber of columnsTwo numbers (rows x columns) describe thedimensions or size of the matrix.Examples:3x3 matrix2x4 matrix1x2 matrix3335144212333010111
Properties of MatricesA matrix is denoted by a bold capital letter and theelements within the matrix are denoted by lower caseletters, e.g. matrix [A] with elements aijmnijmmnijinijaaaaaaaaaaaa21222211211......i goes from 1 to mj goes from 1 to nAmxn=mAn
Properties of MatricesEquality of MatricesTwo matrices are said to be equal only when allcorresponding elements are equalTherefore their size or dimensions are equal aswell325012001325012001A=B=A=B
Properties of MatricesEquality of MatricesSome properties of equality:IIfA=B, thenB=Afor allAandBIIfA=B, andB=C, thenA=Cfor allA,BandC325012001A=B=333231232221131211bbbbbbbbbIfA=Bthenijijba
TYPES OF MATRICES12
Types of Matrices1. Columnmatrix or vector:The number of rows may be any integer but the numberof columns is always 12413112111maaa
Types of Matrices2. Row matrix or vectorAny number of columns but only one row6112530naaaa1131211
Types of Matrices3. Rectangular matrixContains more than one element and number of rows is not equalto the number of columns677773110330200111nm
Types of Matrices4. Square matrixThe number of rows is equal to the number of columns(a square matrix A has an order of m)0311

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