3What you’ll learn about MatricesMatrix Addition and SubtractionMatrix MultiplicationIdentity and Inverse MatricesDeterminant of a Square MatrixApplications… and whyMatrix algebra provides a powerful technique to manipulate large data sets and solve the related problems that are modeled by the matrices.
5Matrix VocabularyEach element, or entry, aij, of the matrix uses double subscript notation.The row subscript is the first subscript i, and the column subscript is j.The element aij is the ith row and the jthcolumn.In general, the order of an m × n matrix ism×n.
22Properties of Matrices Let A, B, and C be matrices whose orders are such thatthe following sums, differences, and products are defined.1. Commutative propertyAddition: A + B = B + AMultiplication: Does not hold in general2. Associative propertyAddition: (A + B) + C = A + (B + C)Multiplication: (AB)C = A(BC)3. Identity propertyAddition: A + 0 = AMultiplication: A·In = In·A = A
23Properties of Matrices Let A, B, and C be matrices whose orders are such thatthe following sums, differences, and products are defined.4. Inverse propertyAddition: A + (-A) = 0Multiplication: AA-1 = A-1A = In |A|≠05. Distributive propertyMultiplication over addition: A(B + C) = AB + AC(A + B)C = AC + BCMultiplication over subtraction: A(B - C) = AB - AC(A - B)C = AC - BC
24Homework:Text pg588/589 Exercises#2, 4, 14, 20, 24, and 34