Q6ts - ⃗v 2 ⃗v 3 ⃗v 4 | | | | = 3 × 6 = 18 2 Find...

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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
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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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