Answer
\[\left[ {\begin{array}{*{20}{c}}
{ - k - 14y} \\
{4z - 8x} \\
{ - 2k + a} \\
{ - 6m + 4n}
\end{array}} \right]\]
Work Step by Step
\[\begin{gathered}
\left[ {\begin{array}{*{20}{c}}
{4k - 8y} \\
{6z - 3x} \\
{2k + 5a} \\
{ - 4m + 2n}
\end{array}} \right] - \left[ {\begin{array}{*{20}{c}}
{5k + 6y} \\
{2z + 5x} \\
{4k + 6a} \\
{2m - 2n}
\end{array}} \right] \hfill \\
{\text{Use the scalar multiplication}} \hfill \\
= \left[ {\begin{array}{*{20}{c}}
{4k - 8y} \\
{6z - 3x} \\
{2k + 5a} \\
{ - 4m + 2n}
\end{array}} \right] + \left[ {\begin{array}{*{20}{c}}
{ - 5k - 6y} \\
{ - 2z - 5x} \\
{ - 4k - 6a} \\
{ - 2m + 2n}
\end{array}} \right] \hfill \\
{\text{Add the corresponding elements}} \hfill \\
= \left[ {\begin{array}{*{20}{c}}
{4k - 8y - 5k - 6y} \\
{6z - 3x - 2z - 5x} \\
{2k + 5a - 4k - 6a} \\
{ - 4m + 2n - 2m + 2n}
\end{array}} \right] \hfill \\
= \left[ {\begin{array}{*{20}{c}}
{ - k - 14y} \\
{4z - 8x} \\
{ - 2k + a} \\
{ - 6m + 4n}
\end{array}} \right] \hfill \\
\end{gathered} \]
