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# s11hw4 - Homework 4 Chapter 2 Section 6 and Chapter 3...

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Homework 4: Chapter 2, Section 6 and Chapter 3, Sections 1, 2, 3 due Monday Feb 14 Notes: 1. For Problem 27, Section 3.1 Use the method of Section 3.2 instead (NOT problem 24) 2. For Problem 30, Section 3.3, just (a) Find Det(A) and (b) find the cofactor of a 2 , 3 (Not the full matrix of cofactors or adj(A)).

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2 Section 3.1 (start Wednesday; finish Friday) Section 3.2 Determinants using row operations (start Wednesday; finish Friday) Section 3.3 Determinates using expansion by minors ((Wednesday)
We compute det 2 1 5 4 2 3 9 5 1 using the (first) row expansion (by minors): det ( A ) = 2 vextendsingle vextendsingle vextendsingle vextendsingle 2 3 5 1 vextendsingle vextendsingle vextendsingle vextendsingle - 1 vextendsingle vextendsingle vextendsingle vextendsingle 4 3 9 1 vextendsingle vextendsingle vextendsingle vextendsingle + 5 vextendsingle vextendsingle vextendsingle vextendsingle 4 2 9 5 vextendsingle vextendsingle vextendsingle vextendsingle = 2(2 - 15) - (4 - 27) + 5(20 - 18) = 2( - 13) - ( - 23) + 5(2) = - 26 + 33 = 7 .

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4 Problem Reduce A = 2 1 3 5 3 0 1 2 4 1 4 3 5 2 5 3 to an upper triagular matrix and use the reduction to find det ( A ) . Solution:
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s11hw4 - Homework 4 Chapter 2 Section 6 and Chapter 3...

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