Question

Find all values of h such that y will be in the subspace spanned by ⟨v₁, v₂⟩ if v₁, v₂ are given vectors and what condition is satisfied?

Answer 1

To determine the values of h for a vector y to be in the subspace spanned by v1 and v2, y must be expressible as a linear combination of v1 and v2. Therefore, h must align with the representation of y in the context of the vectors v1 and v2.

Step-by-step explanation:

To find all values of h such that a vector y will be in the subspace spanned by two given vectors v1 and v2, y must be expressible as a linear combination of v1 and v2. This means that there exist scalars a and b such that y = av1 + bv2. Therefore, h will be dependent on how it is represented within the vector y. The vector y will be in the subspace if it can be represented without requiring additional vectors outside of the span of v1 and v2.