Download e-book for kindle: Elementary linear algebra by Richard O Hill

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By Richard O Hill

ISBN-10: 012348460X

ISBN-13: 9780123484604

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While others may wish simply to accept it and go on. For more details. see Exercises 36 and 37. 5 Gaussian Elimination as a Matrix Factorization 53 We construct A A1 by --+ Adding Adding Adding - 2 times row I to row 2 1 times row 1 to row 3 3 times row J to row 4 8 -3 3 We construct A1 Ai by --+ Adding 1 times row 2 to row 3 Adding 2 times row 2 to row 4 8 1 0 0 -3 -1] We construct Ai A3 = U by -1 4 -2 --+ and L= l ��1 = 1 -2 2 6 Place the negatives of these multiples in the co"esponding positions of L.

Before proving the theorem itself, let us cover that method explicitly. 33). Thus = i , where is the elementary operation associated with or = The method, illustrated in Example 7, chooses the operations in an order that is easiest for most matrices. E 1 , . . - ek · · · e 1 I A - e; Example 7 2 x 2 matrix [: �J Ek Ek· · ·· E· ·1 AE 1 1 Find the inverse of Solution First augment the matrix with the identity, forming [ H 1 -1 0- 3 0 01 20 0 A � I], an n x 2n matrix. �] Chapter 1 Introduction to Linear Equations and Matrices e e Doing a row operation on this matrix corresponds to doing e on A and on simultaneously.

Find elementary matrices E1 and £2 such that E 1 A =Band E2B =A. How 13 I 14 16. 1 7. rices E3 and such that E3B = C and E4C = B. ix is an ele5mentary matrix in two ways . IE1f EE21 iands an E2elementare elareymentmatarriyx. matrices, explain under what circumstances Consider the matrix A = [� �] aaryprmatoductricesof eleandment£2arysumatch trhicatesE2E1 A =I. ((ab)) WrFinidteelAement -1 as . Write A as a product of elementary matrices. find thIen iExernvercseiseifsit2exi1-30,sts. detCheckermiyourne if ansthewgiervenbymatmulrtiixplhasyinganA inA-1verset,oandget -[ -31 �] 22.

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Elementary linear algebra by Richard O Hill

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