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Class Note for MATH 3330 with Professor Flagg at UH


Class Note for MATH 3330 with Professor Flagg at UH

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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 19 views.

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Date Created: 02/06/15
Math 3330 Section 16 006 CO W Matrices An m X Idauix A over a set S is a rectangular array of elements in S arranged in m rows and n columns Shorthand notation A aij mxn Inlongform 0L Ow fL I a QM km 39 MM Dimensionan Square matriximn Diagonal matrix 7 a squ atrix With the nonzero entries only on the main diagonal aLa diagonal Two matrices are equal ifi 5 m 5 I Z a corne spo IVQ in7 e A i riy Me S W Matrix Addition ABC aiijxn bij1mxn Ciijxn CijaijbijIVin 0 cf 6 2 93 6 w Properties of Matrix Addition It is a binary operation on the set of all m by n matrices for any m and n It is associative Anidentity element exists O O 1 Iquot N A Cay M N t I j m A It is commutative Peal NW Every matrix has an additive inverse 14 is comm dialVa Matrix Multiplication aik Jan X bkj1nxp Ci ijxp H Cij Z aikbkj 2 3 k1 I mod rice s capu Lawn Properties of Matiix Multiplication 3 Not a binary operation unless mm oi a 1 L Associative e I An identity element exists for the set MIl S if S has an identity for multiplication e Not all n by n matrices have inverses T I C Multiplication is NOT commutative A N e Distn39butive Propelty holds for Mrl O 6 One 7 Sided Inverses l O I O O t f O7 O O O O O c O 7 1 Example Find two nonzero matIices A and B such that AB 0 I bu flis Find AB ABAB A2 B2 A2 B2 AHQM E C 9 17 W 52 mi xj If i et u exercise 20a amp q r O O H K O 0gt 8 b A W W 88 H3 W1 HR


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