## Elementary Linear Algebra 7th Edition

The set of all $2x2$ matrices of the form $$\left[\begin{array}{ll}{a} & {b} \\ {c} & {1}\end{array}\right]$$ with standard operations is not a vector space. For example, it is not closed under addition, $$\left[\begin{array}{ll}{1} & {0} \\ {1} & {1}\end{array}\right] +\left[\begin{array}{ll}{2} & {1} \\ {0} & {1}\end{array}\right] =\left[\begin{array}{ll}{3} & {1} \\ {1} & {2}\end{array}\right].$$ which is not an element of the set.