Chapter 4 - Vector Spaces - 4.5 Basis and Dimension - 4.5 Exercises - Page 187: 3

\begin{align*} S&=\Bigg{[} \left[\begin{array}{lll}{1} & {0} & {0} &{0}\\ {0} & {0} & {0} &{0}\end{array}\right], \left[\begin{array}{lll}{0} & {1} & {0} &{0}\\ {0} & {0} & {0} &{0}\end{array}\right], \left[\begin{array}{lll}{0} & {0} & {1} &{0}\\ {0} & {0} & {0} &{0}\end{array}\right],\left[\begin{array}{lll}{0} & {0} & {0} &{1}\\ {0} & {0} & {0} &{0}\end{array}\right]\\ & \left[\begin{array}{lll}{0} & {0} & {0} &{0}\\ {1} & {0} & {0} &{0}\end{array}\right], \left[\begin{array}{lll}{0} & {0} & {0} &{0}\\ {0} & {1} & {0} &{0}\end{array}\right], \left[\begin{array}{lll}{0} & {0} & {0} &{0}\\ {0} & {0} & {1} &{0}\end{array}\right],\left[\begin{array}{lll}{0} & {0} & {0} &{0}\\ {0} & {0} & {0} &{1}\end{array}\right]\Bigg{]}. \end{align*}

The standard basis of $M_{2,4}$ is given by \begin{align*} S&=\Bigg{[} \left[\begin{array}{lll}{1} & {0} & {0} &{0}\\ {0} & {0} & {0} &{0}\end{array}\right], \left[\begin{array}{lll}{0} & {1} & {0} &{0}\\ {0} & {0} & {0} &{0}\end{array}\right], \left[\begin{array}{lll}{0} & {0} & {1} &{0}\\ {0} & {0} & {0} &{0}\end{array}\right],\left[\begin{array}{lll}{0} & {0} & {0} &{1}\\ {0} & {0} & {0} &{0}\end{array}\right]\\ & \left[\begin{array}{lll}{0} & {0} & {0} &{0}\\ {1} & {0} & {0} &{0}\end{array}\right], \left[\begin{array}{lll}{0} & {0} & {0} &{0}\\ {0} & {1} & {0} &{0}\end{array}\right], \left[\begin{array}{lll}{0} & {0} & {0} &{0}\\ {0} & {0} & {1} &{0}\end{array}\right],\left[\begin{array}{lll}{0} & {0} & {0} &{0}\\ {0} & {0} & {0} &{1}\end{array}\right]\Bigg{]}. \end{align*}