Question

Find a linearly independent set of vectors that spans the same subspace

A) A set of vectors that is not linearly independent.
B) A set of vectors with no common subspace.
C) A set of vectors that forms a linearly independent basis.
D) Linearly independent vectors cannot span the same subspace.

Answer 1

The correct answer is C) A set of vectors that forms a linearly independent basis.

Step-by-step explanation:

The correct answer is C) A set of vectors that forms a linearly independent basis.

When we say that a set of vectors spans a subspace, it means that every vector in that subspace can be expressed as a linear combination of the vectors in the set. When we say that a set of vectors is linearly independent, it means that no vector in the set can be expressed as a linear combination of the other vectors in the set.

So, a set of vectors that forms a linearly independent basis will span the same subspace because every vector in the subspace can be expressed as a linear combination of the basis vectors, and the basis vectors themselves are not linearly dependent on each other.