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Quiz VI
1. Suppose that
⃗v
1
,
⃗v
2
,
⃗v
3
,
⃗v
4
are vectors in
R
4
and
det




⃗v
1
⃗v
2
⃗v
3
⃗v
4




= 6
.
Find the values of the following
i) det




⃗v
1
⃗v
2
⃗v
3
+ 2
⃗v
1
6
⃗v
1




The last column is 6 times the ﬁrst column, so this is 0.
ii) det




⃗v
3

⃗v
2
⃗v
1

⃗v
4




This has one swap and two columns multiplied by 1. So it is 6.
iii) det




3
⃗v
1
+ 2
⃗v
2
+ 3
⃗v
3
⃗v
2
+ 3
⃗v
3
⃗v
3
+ 4
⃗v
4
⃗v
4




.
This is the same as
det




3
⃗v
1
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Unformatted text preview: ⃗v 2 ⃗v 3 ⃗v 4     = 3 × 6 = 18 . 2. Find the area of the parallelogram in R 3 deﬁned by ⃗v 1 = 2 5 1 and ⃗v 2 = 1 2 . Solution. If you set A equal to the matrix with columns ⃗v 1 and ⃗v 2 , this is the square root of the determinant of A T A . That is ( det ( 30 4 4 5 )) 1 / 2 = √ 134 ....
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This note was uploaded on 02/06/2011 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.
 Fall '08
 lee
 Vectors

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