Question

 Use row reduction to determine whether the set of vectors {(1,2,0), (0,1,-1),(1,1,2)} is linearly independent in                                                                 

Answer 1

$\left( {\begin{matrix} 1&2&0\\ 0&1&{ - 1}\\ 1&1&2 \end{matrix}} \right)\begin{matrix} {}\\ {}\\ { - I} \end{matrix} \sim \left( {\begin{matrix} 1&2&0\\ 0&1&{ - 1}\\ 0&{ - 1}&2 \end{matrix}} \right)\begin{matrix} {}\\ {}\\ { + II} \end{matrix} \sim \left( {\begin{matrix} 1&2&0\\ 0&1&{ - 1}\\ 0&0&1 \end{matrix}} \right)$

Since the rank of the resulting matrix is ​​3, the system of these vectors is linearly independent