Question

If {u, v, w} CR" is a set of linearly dependent vectors, then any one of these three vectors can be written as a linear combination of the other two. Select one:

True.
False.

Answer 1

The statement is True. If a set of vectors {u, v, w} is linearly dependent, then it means that one vector can be written as a linear combination of the other two.

Step-by-step explanation:

The statement is True. If a set of vectors {u, v, w} is linearly dependent, then it means that one vector can be written as a linear combination of the other two. In this case, let's say u can be written as a linear combination of v and w. This means that u = av + bw, where a and b are scalars.

The same can be done for v and w as well. For example, v can be written as a linear combination of u and w, and w can be written as a linear combination of u and v.

Therefore, any one of the vectors u, v, or w can be expressed as a linear combination of the other two.