1Matrices Properties, Operations, AlgebraMatrices and their properties•A matrix is a rectangular array of numbers; an m x nmatrixhasmrows andncolumnsm x n has rows and n columns •Ifm = nwe call it a square matrix•A zero matrix is one which has zero entries everywhere•Two matrices are equal if they have the same idll th it ilsize and all their entries are equalMatrices and their properties•Column matrix: ism x 1•Row matrix: is1 x n•scalar multiple of a matrix : kA, where each entry is multiplied by kOperations on matrices: Addition/Subtraction•Two matrices can be addedor subtractedif they have the same size; A + B , A - B•The result is obtained just by adding or subtracting individual entries
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2Operations on matrices: Multiplication•The product ABof two matrices is defined only if the left matrix, A, has the same number of columns as the right matrix, B, has rows•m x rcan multiply r x nto give m x n•Note the order matters!!Operations on matrices: Multiplication•If Ais anm x rmatrix, and B is an r x nmatrix, then the product AB = Cis the m x nmatrix whose entries are determined as follows: •to find the entry in row i, column jof AB–single out row ifrom the matrix Aand column jfrom the matrix B–multiply together the corresponding entries from the row and column–add up the resulting products.Example: Product of 2 matrices •A: 2 x 4, B: 4 x 7, C: 7 x 2 –can give 9 potential products of which only 3 arecan give 9 potential products, of which only 3 are definedMatrix multiplication example121231133143112