onsider a linearly independent spanning set v1, . . . , vn. Consider a subset v1, . . . , vm, wherem < n. Is v1, . . . , vm spanning or not spanning? In your answer, you may use definitions andproperties of linearly independent sets and spanning sets, but not the concepts of a basis anddimension

The subset v1, . . . , vm, where m < n, is not necessarily a spanning set.

A spanning set is a set of vectors that can be linearly combined in various ways to get any vector in the given vector space. In other words, a set of vectors spans a space if you can reach any point in the space by scaling and adding the vectors in the set.

Given a linearly independent spanning set v1, . . . , vn, it means that any vector in the space can be written as a linear combination of these vectors. However, if we only take a subset of these vectors, v1, . . . , vm, where m < n, we are removing some vectors from our original set.

This means that there may be some vectors in the space that we can no longer reach with a linear combination of the vectors in our subset. Therefore, the subset v1, . . . , vm is not necessarily a spanning set for the space.

However, it's important to note that it could still be a spanning set for a smaller subspace. Whether or not it is a spanning set depends on the specific vectors in the set and the space in question.