Answer
$Standard\space Matrix,\space A =[^{\matrix{\space\space\space1}\matrix{0}}_{\matrix{-2}\matrix{1}}]$
Work Step by Step
Given question:
$T : R^{1}->R^{2}$ is a vertical shear transformation that maps $e_{1}$ into $e_{1} - 2e_{2}$ but leaves the vector $e_{2}$ unchanged.
$T(e_{1})=e_{1}-2e_{2}=[^{\matrix{1}}_{\matrix{0}}]-2[^{\matrix{0}}_{\matrix{1}}]=[^{\matrix{\space\space1}}_{\matrix{-2}}]$
$T(e_{2})=e_{2}=[^{\matrix{0}}_{\matrix{1}}]$
$Standard\space Matrix,\space A =[^{\matrix{\space\space1}\matrix{\space0}}_{\matrix{-2}\matrix{1}}]$
