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Homework 12.4-solutions

# Homework 12.4-solutions - mehmood(ajm4462 Homework 12.4...

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mehmood (ajm4462) – Homework 12.4 – karakurt – (56295) 1 This print-out should have 16 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 2 3 2 2 v v v v v x 2 + v v v v v 3 2 2 2 v v v v v x . 1. f ( 2) = 66 2. f ( 2) = 60 correct 3. f ( 2) = 68 4. f ( 2) = 62 5. f ( 2) = 64 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 2 3 2 2 v v v v v x 2 + v v v v v 3 2 2 2 v v v v v x = ((2) ( 2) (2) (3)) x 2 + ((3) (2) (2) ( 2)) x . Consequently, f ( x ) = 10 x 2 + 10 x , and so f ( 2) = 60 . keywords: determinant 002 10.0 points By evaluating the determinant, express f ( x ) = v v v v v v 1 x x 2 3 2 0 4 2 3 v v v v v v as a quadratic Function in x . 1. f ( x ) = 6 9 x 2 x 2 2. f ( x ) = 6 + 2 x 9 x 2 3. f ( x ) = 6 + 9 x 2 x 2 correct 4. f ( x ) = 6 9 x + 2 x 2 5. f ( x ) = 6 + 9 x + 2 x 2 6. f ( x ) = 6 2 x + 9 x 2 Explanation: ±or this 3 × 3 determinant, use expansion by minors along the top row: f ( x ) = v v v v 2 0 2 3 v v v v v v v v 3 0 4 3 v v v v x + v v v v 3 2 4 2 v v v v x 2 . Evaluating the 2 × 2 determinants, we thus see that f ( x ) = 6 + 9 x 2 x 2 . keywords: matrix, determinant, quadratic Function, expansion by minors 003 10.0 points ±ind the value oF the determinant D = v v v v v v v 2 1 3 x y z 3 2 1 v v v v v v v . 1. D = 7 x + 7 y + 7 z correct 2. D = 7 x + 7 y + 7 z 3. D = 7 x 7 y 7 z 4. D = 7 x + 7 y 7 z 5. D = 7 x 7 y 7 z

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mehmood (ajm4462) – Homework 12.4 – karakurt – (56295) 2 6. D = 7 x 7 y + 7 z Explanation: For any 3 × 3 determinant v v v v v v v A B C a 1 b 1 c 1 a 2 b 2 c 2 v v v v v v v = A v v v v v b 1 c 1 b 2 c 2 v v v v v B v v v v v a 1 c 1 a 2 c 2 v v v v v + C v v v v v a 1 b 1 a 2 b 2 v v v v v . Thus D = v v v v v v v 2 1 3 x y z 3 2 1 v v v v v v v = 2 v v v v v y z 2 1 v v v v v + v v v v v x z 3 1 v v v v v + 3 v v v v v x y 3 2 v v v v v = 2 ( y + 2 z ) + ( x + 3 z ) + 3 ( 2 x + 3 y ) . Consequently, D = 7 x + 7 y + 7 z . keywords: determinant 004 10.0 points Find the cross product of the vectors a = i 2 j 3 k , b = 3 i + j k . 1. a × b = 6 i + 8 j 7 k 2. a × b = 5 i + 8 j 7 k correct 3. a × b = 6 i 3 j 8 k 4. a × b = 5 i 4 j 8 k 5. a × b = 5 i 3 j 7 k 6. a × b = 6 i + 8 j 8 k Explanation: One way of computing the cross product ( i 2 j 3 k ) × ( 3 i + j k ) is to use the fact that i × j = k , j × k = i , k × i = j , while i × i = 0 , j × j = 0 , k × k = 0 .
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Homework 12.4-solutions - mehmood(ajm4462 Homework 12.4...

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