Respuesta :
Answer:
Step-by-step explanation:
We will solve this questions using some dimensionality analysis.
a) Note that [tex]\mathbb{R}^4[/tex] is a vector space of dimension 4. So, given a set of three vectors, they could be or could not be linearly independent. However, if they were, they would not span [tex]\mathbb{R}^4[/tex] since in order for us to span [tex]\mathbb{R}^4[/tex] we need 4 or more vectors. Since a set of three vector cannot span this space, they automatically cant be a basis for [tex]\mathbb{R}^4[/tex].
b) [tex]\mathbb{R}^3[/tex] has a dimension 3. So, for a set of vectors A to span this space, we need that A contains at least 3 vectors that are linearly independent. So A could have possibly infinite number of vectors as long as there is a subset of A that is composed by 3 linearly independent vectors.
