Suppose \(\vec {v}_1, \vec {v}_2, \vec {v}_3\) and \(\vec {w}\) are vectors in \(\RR ^n\). What are the implications of the statement: \(\vec {w}\) is in the span of \(\vec {v}_1, \vec {v}_2, \vec {v}_3\) Select all that apply.
Vector \(\vec {w}\) a linear combination of \(\vec {v}_1, \vec {v}_2, \vec {v}_3\) The set \(\{\vec {v}_1, \vec {v}_2, \vec {v}_3, \vec {w}\}\) contains redundant vectors. Vectors \(\vec {v}_1, \vec {v}_2, \vec {v}_3, \vec {w}\) are linearly independent. Vectors \(\vec {v}_1, \vec {v}_2, \vec {v}_3, \vec {w}\) are linearly dependent. Vector \(\vec {v}_1\) can be written as a linear combination of \(\vec {v}_2, \vec {v}_3, \vec {w}\). The equation \(a\vec {v}_1+ b\vec {v}_2+ c\vec {v}_3+ d\vec {w}=\vec {0}\) has a non-trivial solution.