Chapter2a.pdf - CHAPTER 2a MATRICES u2022 A J Clark School...

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1° A. J. Clark School of Engineering °Department of Civil and Environmental EngineeringbyDr. Ibrahim A. AssakkafSpring 2001ENCE 203 - Computation Methods in Civil Engineering IIDepartment of Civil and Environmental EngineeringUniversity of Maryland, College ParkCHAPTER 2a.MATRICES' AssakkafSlide No. 1° A. J. Clark School of Engineering ° Department of Civil and Environmental EngineeringENCE 203 ° CHAPTER 2a. MATRICESIntroductionDefinition of a MatrixA matrixis a rectangular array of elements arranged in a horizontal rows and vertical columns.
2' AssakkafSlide No. 2° A. J. Clark School of Engineering ° Department of Civil and Environmental EngineeringENCE 203 ° CHAPTER 2a. MATRICESIntroductionExamples:102531240123114+25ln2xxdxdexxxEIPLdLEwLdLEwLdL642434243422113211321θθθθθθ5.192πqualifiedfair48democratqualifiednot good37republican' AssakkafSlide No. 3° A. J. Clark School of Engineering ° Department of Civil and Environmental EngineeringENCE 203 ° CHAPTER 2a. MATRICESIntroductionGeneral Form of a Matrixrcrrrcccaaaaaaaaaaaaaaaa............321333323122322211131211MMMMM(1)
3' AssakkafSlide No. 4° A. J. Clark School of Engineering ° Department of Civil and Environmental EngineeringENCE 203 ° CHAPTER 2a. MATRICESIntroductionGeneral Form of a Matrix° Each column has the same number of values rr= number of rows° Each row has the same number of values cc = number of columns° It is not necessary for the number of rows to equal the number of columns' AssakkafSlide No. 5° A. J. Clark School of Engineering ° Department of Civil and Environmental EngineeringENCE 203 ° CHAPTER 2a. MATRICESIntroductionGeneral From of a Matrix° Notations and Convention±A capital letter can be used to denote the name of an array or a matrix.±The values contained in the matrix are called elements and are denoted as aij=333122211211aaaaaaA=333122211211Mmmmmmm
4' AssakkafSlide No. 6° A. J. Clark School of Engineering ° Department of Civil and Environmental EngineeringENCE 203 ° CHAPTER 2a. MATRICESIntroductionGeneral From of a Matrix° Notations and Convention±A matrix can also be abbreviated using the following notations:±In this notation, aijrepresents the general element of the matrix and appears in the ithrow and jthcolumn.

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