linear combination problem dealing with uniqueness
Let be a vector space and with the property that whenever and , then . Prove that every vector in the span of can be uniquely written as a linear combination of vectors in .
Let be a vector space and with the property that whenever and , then . Prove that every vector in the span of can be uniquely written as a linear combination of vectors in .
So, let such that and . Then . This means that . From the hypothesis, . Therefore,