## Elementary Linear Algebra 7th Edition

Consider the combination $$a \left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right]+b\left[\begin{array}{cc}{0} & {1} \\ {0} & {0}\end{array}\right]+c\left[\begin{array}{ll}{0} & {0} \\ {0} & {0}\end{array}\right]=0, \quad a,b,c\in R.$$ Which yields the following system of equations \begin{align*} a&=0\\ b&=0. \end{align*} Then the set of vectors is linearly independent set of vectors.