Final answer:
If x and y are linearly independent, and if {x, y, z} is linearly dependent, then z is in span{x, y}.
Step-by-step explanation:
True.
If x and y are linearly independent, it means that neither vector can be expressed as a linear combination of the other. This means that the span of x and y is a two-dimensional subspace, represented by a plane in three-dimensional space.
If {x, y, z} is linearly dependent, it means that the vector z can be expressed as a linear combination of x and y. Therefore, z is in the span of x and y.