Linear Combination
Definition
Let \(S\subset V\), let \(v\in V\) we say \(v\) is a linear combination of vectors of \(S\) if \(\exists v_1, v_2, ..., v_n\in S\) and \(\exists a_1, ..., a_n\in F\) st. \(v=a_1v_1+...+a_nv_n\)
Let \(S\subset V\), let \(v\in V\) we say \(v\) is a linear combination of vectors of \(S\) if \(\exists v_1, v_2, ..., v_n\in S\) and \(\exists a_1, ..., a_n\in F\) st. \(v=a_1v_1+...+a_nv_n\)