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Learning ObjectivesDescribe the parts of a matrix and what they representKey TakeawaysKey Points•A matrix (whose plural is matrices) is a rectangular array of numbers, symbols, or expressions,arranged in rows and columns.•A matrix with mm rows and nn columns is called an m×nm×n matrix or mm-by-nn matrix, wheremm and nn are called the matrix dimensions.•Matrices can be used to compactly write and work with multiple linear equations, that is, a system oflinear equations. Matrices and matrix multiplication reveal their essential features when related tolinear transformations, also known as linear maps.Key Terms•element: An individual item in a matrix•row vector: A matrix with a single row•column vector: A matrix with a single column•square matrix: A matrix which has the same number of rows and columns•matrix: A rectangular array of numbers, symbols, or expressions, arranged in rows and columns
History of the MatrixThe matrix has a long history of application in solving linear equations. They were known as arrays until the18001800‘s. The term “matrix” (Latin for “womb”, derived frommater—mother) was coined by JamesJoseph Sylvester in 18501850, who understood a matrix as an object giving rise to a number of determinantstoday called minors, that is to say, determinants of smaller matrices that are derived from the original one byremoving columns and rows. An English mathematician named Cullis was the first to use modern bracketnotation for matrices in 19131913 and he simultaneously demonstrated the first significant use of the notationA=ai,jA=ai,j to represent a matrix where ai,jai,j refers to the element found in theith row and thejth column.Matrices can be used to compactly write and work with multiple linear equations, referred to as a system oflinear equations, simultaneously. Matrices and matrix multiplication reveal their essential features whenrelated to linear transformations, also known as linear maps.What is a MatrixIn mathematics, amatrix(plural matrices) is a rectangular array of numbers, symbols, or expressions,arranged in rows and columns. Matrices are commonly written in box brackets. The horizontal and verticallines of entries in a matrix are calledrowsandcolumns, respectively. The size of a matrix is defined by thenumber of rows and columns that it contains. A matrix withmrows andncolumns is called anm×nmatrixor mm-by-nn matrix, whilemandnare called itsdimensions.The dimensions of the following matrix are2×32×3 up(read “two by three”), because there are two rows and three columns.