Answer
$$
0=\left[\begin{array}{rrrr}{0} & {0} & {0} & {0} \\ {0} & {0} & {0} & {0} \\ {0} & {0} & {0} & {0}\end{array}\right].
$$
$$-u=\left[\begin{array}{rrrr}{-a_{11}} & {-a_{12}} & {-a_{13}} & {-a_{14}} \\ {-a_{21}} & {-a_{22}} & {-a_{23}} & {-a_{24}} \\ {-a_{31}} & {-a_{32}} & {-a_{33}} & {-a_{34}}\end{array}\right].$$
Work Step by Step
The zero vector of the vector space $M_{3,4}$ is given by
$$
0=\left[\begin{array}{rrrr}{0} & {0} & {0} & {0} \\ {0} & {0} & {0} & {0} \\ {0} & {0} & {0} & {0}\end{array}\right].
$$
Let $u$ be an vector in $M_{3,4}$ such that
$$u=\left[\begin{array}{rrrr}{a_{11}} & {a_{12}} & {a_{13}} & {a_{14}} \\ {a_{21}} & {a_{22}} & {a_{23}} & {a_{24}} \\ {a_{31}} & {a_{32}} & {a_{33}} & {a_{34}}\end{array}\right].$$
Now, the additive inverse of $u$ is given by
$$-u=\left[\begin{array}{rrrr}{-a_{11}} & {-a_{12}} & {-a_{13}} & {-a_{14}} \\ {-a_{21}} & {-a_{22}} & {-a_{23}} & {-a_{24}} \\ {-a_{31}} & {-a_{32}} & {-a_{33}} & {-a_{34}}\end{array}\right].$$
