The set of three vectors does not span [tex]\mathbb{R} ^4[/tex].
Given that [tex]Dim(\mathbb{R} ^4)=4[/tex]
If [tex]\mathbb{R} ^4=span(\mathbb{S} )[/tex] then [tex]Dim(\mathbb{R} ^4)=Dim (\mathbb{S})=4[/tex]
But a set containing three vectors can have the maximum dimension but not equal to 4.
Therefore, the set of three vectors does not span [tex]\mathbb{R} ^4[/tex].
Similarly, the set of [tex]n[/tex] does not span [tex]\mathbb{R} ^m[/tex] with [tex]nLearn More:https://brainly.com/question/5294978
