Test 2 Review

# Test 2 Review - MA 405-003 Test 2 Review Test 2 covers 2.1...

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Unformatted text preview: MA 405-003 Test 2 Review Test 2 covers 2.1, 2.2, 2.3, 3.1, 3.2. 1. Know theorems and definitions, including: (a) determinant (p. 95), adj ( A ), A ( adj ( A )) = det ( A ) · I , det ( adj ( A )) = ( det ( A )) n- 1 , Cramer’s Rule, Vector Space, Subspace, Nullspace, span and spanning set (pp. 128-129) (b) Theorems 2.1.1, 2.1.2, 2.1.3, 2.1.4, 2.2.1, 2.2.2, 2.2.3, how row operations alter determinant, det ( kA ) = k n det ( A ), Subpace Test: If V =vector space and S ⊆ V ( S non-empty) then: S = subspace ⇔ u + v S, ku S ; ∀ u, v S, ∀ k R 3.2.1 2. Example problems (a) 2.1 (p. 97) #3, 4, 5, 6 (answers in back) (b) 2.2 (p. 104) #4 det( A ) = (1 · 9 · 3+1 · c · 1+1 · 1 · c )- (1 · 9 · 1+ c · c · 1+3 · 1 · 1) = (27+2 c )- (12+ c 2 ) =- c 2 + 2 c + 15 A singular if det( A ) = 0, which happens when c 2- 2 c- 15 = 0 so ( c +3)( c- 5) = 0, rather c =- 3 , 5. (c) 2.2 #16 A T =- A ⇒ det( A T ) = det(- A ) ⇒ det( A ) = (- 1) n det( A ) n odd ⇒ det( A ) =- det( A ) ⇒ 2 det(...
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Test 2 Review - MA 405-003 Test 2 Review Test 2 covers 2.1...

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