$Do you mean something like this\?$
$Suppose we have a set$ \;S = \{v_{1}, v_{2}, ..., v_{n}\} \;$of linearly independent vectors and a set$\; T = \{w_{1},....,w_{m}\}\; $where for each$ \;T\; $is a linear combination of elements of$\; S \;$with$\; m > n. \; $Then$\; T \;$is linearly independent.$