Question : Find null space of the following vectors and determine linearly dependent or independent?1. \[\left(\begin{matrix}1\\1\\1\\\end{matrix}\right),\left(\begin{matrix}1\\2\\3\\\end{matrix}\right),\left(\begin{matrix}2\\3\\1\\\end{matrix}\right)\] 2. \[\left(\begin{matrix}-3\\1\\3\\\end{matrix}\right),\left(\begin{matrix}1\\2\\8\\\end{matrix}\right),\left(\begin{matrix}-3\\4\\18\\\end{matrix}\right)\]3. \[\left(\begin{matrix}1\\-2\\1\\\end{matrix}\right),\left(\begin{matrix}2\\1\\0\\\end{matrix}\right),\left(\begin{matrix}3\\0\\1\\\end{matrix}\right)\]Solution :Null space : Null space is the set of column vectors of the row reduced matrix of the matrix formed by…
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