Texts: A set of vectors {v1, v2, ..., vn} in a vector space V is called linearly dependent if we can find scalars t1, t2, ..., tn, not all zero, such that t1v1 + t2v2 + ... + tnvn = 0, where the right hand side is the zero vector.
To demonstrate that a given set of vectors is linearly dependent, it is a good idea to use the definition and row reduction to explicitly find scalars that demonstrate the linear relation.
If our investigation leads us to conclude that the only way to arrange a linear relation with the right hand side being 0 is to use t1 = t2 = ... = tn = 0, then the set cannot be linearly dependent (i.e. the set is a linearly independent set).
Let's show that
-13 3 -16
2
3
is actually a linearly dependent set by finding scalars r, s, and t (not all zero) such that ru + sv + tw = 0.
For example:
r s t
0 0 0
Using this, we can express one of the vectors as a linear combination of the others, for example, v = 4u - 3w.
Note: There are three valid answers for this last part. If your answer is v = 10u - 11w, then you should enter it using the syntax v = 10*u - 11*w (note: this isn't actually the answer).
