Which of the following sets of vectors in R3 are linearly dependent? Note. Mark all your choices.

9514 1404 393

  B, C

Step-by-step explanation:

Linearly dependent sets can be found using row-reduction techniques. If a row ends up zero, then the set is linearly dependent. Equivalently, the determinant of a 3×3 matrix can be computed. If it is zero, the set is dependent. The cross-product of two 3-D vectors can be computed. If it is zero, the vectors are dependent.

Any set of vectors that has more elements than each vector does must necessarily be dependent.

It is helpful to be able to use a calculator capable of performing these calculations (as opposed to doing it by hand). The first attachment shows the result of computing the reduced row-echelon form of the first set of 3 vectors. The set is found to be independent.

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The second set of vectors is clearly dependent, as the second vector is 5 times the first.

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The third set contains more vectors than there are elements to a vector. Hence at least one of them can be created using some combination of the others. This set is dependent.

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The cross-product of the fourth set is non-zero, so it is independent. The second attachment shows the result of a row-reduction tool on these vectors.

think the answer would beb