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Unformatted text preview: (−2) = −60 . keywords: matrix, determinant, quadratic
function, expansion by minors
003 10.0 points Find the value of the determinant
2
D= x
−3 −1
y z −2 −1 2. D = 7x + 7y + 7z
10.0 points By evaluating the determinant, express
f ( x) = 1
3
−4 . 1. D = −7x + 7y + 7z correct keywords: determinant
002 3 x
−2
2 x2
0
−3 3. D = 7x − 7y − 7z
4. D = 7x + 7y − 7z
5. D = −7x − 7y − 7z mehmood (ajm4462) – Homework 12.4 – karakurt – (56295)
Explanation:
One way of computing the cross product 6. D = −7x − 7y + 7z Explanation:
For any 3 × 3 determinant
A B C a1 b1 c1 a2 b2 c2 =A 2 (−i − 2j − 3k) × (−3i + j − k)
is to use the fact that b1 c1 b2 c2 i × j = k, j×k = i, k ×i = j, j×j = 0, k× k = 0. while −B a1 c1 a2 c2 −1
y −2
z −2 −1 a2 b2 −1 y b1 z −3 a1 3 +C . i× i = 0,
For then Thus
2
D= =2 x + a × b = 5i + 8j − 7k .
Alternatively, we can use the deﬁnition
x z −3 −1 +3 x y −3 −2 = 2 (−y + 2z ) + (−x + 3z ) + 3 (−2x + 3y ) . i
−1
−3 a×b = −2
1 = Consequently, j
−2
1 −1
−3
i−
−3
−1...
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 Spring '10
 odell

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