Introduction to MatricesWhat is a Matrix?A matrix is a rectangular arrays of numbers, symbols, or expressions, arranged inrows and columns.LEARNING OBJECTIVESDescribe the parts of a matrix and what they representKEY TAKEAWAYSKey PointsA matrix (whose plural is matrices) is a rectangular array of numbers,symbols, or expressions, arranged in rows and columns.A matrix withmmrows andnncolumns is called anm×nm×nmatrixormm-by-nnmatrix, wheremmandnnare called the matrix dimensions.Matrices can be used to compactly write and work with multiple linearequations, that is, a system of linear equations. Matrices and matrixmultiplication reveal their essential features when related to lineartransformations, also known as linear maps.Key Termselement: An individual item in a matrixrow vector: A matrix with a single rowcolumn vector: A matrix with a single columnsquare matrix: A matrix which has the same number of rows and columnsmatrix: A rectangular array of numbers, symbols, or expressions,arranged in rows and columnsHistory of the MatrixThe matrix has a long history of application in solving linear equations. They wereknown as arrays until the18001800‘s. The term “matrix” (Latin for “womb”,derived frommater—mother) was coined by James Joseph
Sylvester in18501850, who understood a matrix as an object giving rise to anumber of determinants today called minors, that is to say, determinants ofsmaller matrices that are derived from the original one by removing columns androws. An English mathematician named Cullis was the first to use modernbracket notation for matrices in19131913and he simultaneously demonstratedthe first significant use of the notationA=ai,jA=ai,jto represent a matrixwhereai,jai,jrefers 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 of linear equations, simultaneously. Matrices and matrixmultiplication reveal their essential features when related to lineartransformations, 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 commonlywritten in box brackets. The horizontal and vertical lines of entries in a matrix arecalledrowsandcolumns, respectively. The size of a matrix is defined by thenumber of rows and columns that it contains. A matrix withmrowsandncolumns is called anm×nmatrix ormm-by-nnmatrix, whilemandnarecalled itsdimensions.The dimensions of the following matrixare2×32×3up(read “two by three”), because there are two rows and threecolumns.