4.1 Determinants - 4.1 4 Determinants 4.1 Determinants of...

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Unformatted text preview: 4.1. § 4. Determinants 4.1. Determinants of Order 2 1. (a) F det( A + B ) 6 = det( A ) + det( B ) (b) T (p.200. Theorem 4.1) (c) F (p.201. Theorem 4.2) (d) F The area of the paralleogram determined by u and v equals O u v ¶ det u v ¶ (e) F (p.203) 2. (a) 30 (b) -17 (c) -8 3. (a) -10+15i (b) 36+41i (c) -24 4. (a) 4 (b) 10 (c) 14 (d) 26 188 PNU-MATH 4.1. 5. Let A = a 11 a 12 a 21 a 22 ¶ , then B = a 21 a 22 a 11 a 12 ¶ So det( B ) = a 12 a 21- a 11 a 22 =- ( a 11 a 22- a 12 a 21 ) =- det( A ) 6. Let A = a a b b ¶ , and B = b b a a ¶ By the exercise 15, det( B ) =- det( A ) Since det( A ) = det( B ) ∴ det( A ) = 0 7. Let A = a 11 a 12 a 21 a 22 ¶ , then A t = a 11 a 21 a 12 a 22 ¶ det( A t ) = a 11 a 22- a 21 a 12 = det( A ) ∴ det( A t ) = det( A ) 8. If A = a 11 a 12 a 22 ¶ , then det( A ) = a 11 a 22 : the product of the diagonal entries of A 9. Let A = a 11 a 12 a 21 a 22 ¶ and B = b 11 b 12 b 21 b 22 ¶ 189 PNU-MATH 4.1....
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This note was uploaded on 02/14/2012 for the course MAS 4105 taught by Professor Rudyak during the Spring '09 term at University of Florida.

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4.1 Determinants - 4.1 4 Determinants 4.1 Determinants of...

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