4.1 Determinants

# 4.1 Determinants - 4.1 Â 4 Determinants 4.1 Determinants of...

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Unformatted text preview: 4.1. Â§ 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 Â¶ det u v Â¶ (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 Â¶ , then B = a 21 a 22 a 11 a 12 Â¶ 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 Â¶ , and B = b b a a Â¶ By the exercise 15, det( B ) =- det( A ) Since det( A ) = det( B ) âˆ´ det( A ) = 0 7. Let A = a 11 a 12 a 21 a 22 Â¶ , then A t = a 11 a 21 a 12 a 22 Â¶ det( A t ) = a 11 a 22- a 21 a 12 = det( A ) âˆ´ det( A t ) = det( A ) 8. If A = a 11 a 12 a 22 Â¶ , 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 Â¶ and B = b 11 b 12 b 21 b 22 Â¶ 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 Â 4 Determinants 4.1 Determinants of...

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