HW21 - Sect. 12.4-solutions

HW21 - Sect. 12.4-solutions - cai(atc667 HW21 Sect 12.4...

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cai (atc667) – HW21 - Sect. 12.4 – chavez-dominguez – (55235) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points ±ind the value oF f ( 2) when f ( x ) = v v v v v 1 2 2 3 v v v v v x 2 + v v v v v 2 3 1 2 v v v v v x . 1. f ( 2) = 6 correct 2. f ( 2) = 10 3. f ( 2) = 4 4. f ( 2) = 12 5. f ( 2) = 8 Explanation: ±or any 2 × 2 determinant v v v v v a b c d v v v v v = ad bc . Thus f ( x ) = v v v v v 1 2 2 3 v v v v v x 2 + v v v v v 2 3 1 2 v v v v v x = (( 1) (3) (2) ( 2)) x 2 + (( 2) (2) ( 1) (3)) x . Consequently, f ( x ) = x 2 1 x , and so f ( 2) = 6 . keywords: determinant 002 10.0 points By evaluating the determinant, express f ( x ) = v v v v v v 1 x x 2 4 3 2 0 4 1 v v v v v v as a quadratic Function in x . 1. f ( x ) = 11 16 x 4 x 2 2. f ( x ) = 11 4 x + 16 x 2 3. f ( x ) = 11 + 4 x + 16 x 2 4. f ( x ) = 11 + 4 x 16 x 2 5. f ( x ) = 11 + 16 x + 4 x 2 6. f ( x ) = 11 4 x 16 x 2 correct Explanation: ±or this 3 × 3 determinant, use expansion by minors along the top row: f ( x ) = v v v v 3 2 4 1 v v v v v v v v 4 2 0 1 v v v v x + v v v v 4 3 0 4 v v v v x 2 . Evaluating the 2 × 2 determinants, we thus see that f ( x ) = 11 4 x 16 x 2 . keywords: matrix, determinant, quadratic Function, expansion by minors 003 10.0 points Which oF the Following expressions are well- defned For all vectors a , b , c , and d ? I ( a × b ) · ( c × d ) , II a · ( b × c ) , III | a | × ( b × c ) . 1. none oF them 2. II only 3. I and III only 4. I and II only correct

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cai (atc667) – HW21 - Sect. 12.4 – chavez-dominguez – (55235) 2 5. all of them 6. I only 7. II and III only 8. III only Explanation: The cross product is deFned only for two
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HW21 - Sect. 12.4-solutions - cai(atc667 HW21 Sect 12.4...

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