Since the trace can only be calculated for $\displaystyle n\times n$ matrices, the trace isn't possible to calculate.

In order to calculate the trace, we need to sum up each entry along the main diagonal.

$\displaystyle Trace=-3+25-22=0$

By definition, 

$\displaystyle tr(A)= \sum_{i=1}^n a_{ii}$.

Therefore, 

$\displaystyle tr(A)= 0+0+(-3)+4=1$.

By definition, the trace of a matrix only exists in the matrix is a square matrix.  In this case, $\displaystyle A$ is not square.  Therefore, the trace does not exist.

$\displaystyle \begin{align*}&\text{We can find the trace of a square nxn matrix by summing its diagonal elements:}\\&\sum_{i=1}^{n}A_{i,i}\\&\text{i.e. }Tr\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}=a+e+i\\&\text{For }A=\begin{bmatrix}-8&-7\\-3&0\end{bmatrix}\\&(-8)+(0)=-8\end{align*}$

$\displaystyle \begin{align*}&\text{Tr in the context of linear algebra represents the trace.}\\&\text{We can find this quantity for a square nxn matrix by summing the elements of its diagonal:}\\&\sum_{i=1}^{n}A_{i,i}\\&\text{i.e. }Tr\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}=a+e+i\\&\text{Doing so we find for}\begin{bmatrix}-10&-7\\7&-15\end{bmatrix}\\&\text{We find:}\\&(-10)+(-15)=-25\end{align*}$

$\displaystyle \begin{align*}&\text{Tr in the context of linear algebra represents the trace.}\\&\text{We can find this quantity for a square nxn matrix by summing the elements of its diagonal:}\\&\sum_{i=1}^{n}A_{i,i}\\&\text{i.e. }Tr\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}=a+e+i\\&\text{Doing so we find for}\begin{bmatrix}-7&8&-12&-19&10&0&-1&17\\5&5&15&13&3&-13&-11&16\\-19&0&-14&20&9&0&-1&-18\\7&-19&-18&1&-17&13&13&9\\-14&7&1&19&6&12&-2&-3\\13&-17&-15&-13&-4&14&12&-18\\-4&1&-3&6&5&-9&-3&-20\\20&-14&-16&-5&-12&0&-7&19\end{bmatrix}\\&\text{We find:}\\&(-7)+(5)+(-14)+(1)+(6)+(14)+(-3)+(19)=21\end{align*}$

$\displaystyle \begin{align*}&\text{We can find the trace of a square nxn matrix by summing its diagonal elements:}\\&\sum_{i=1}^{n}A_{i,i}\\&\text{i.e. }Tr\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}=a+e+i\\&\text{For }A=\begin{bmatrix}20&-8&8&7\\2&8&7&-13\\-15&20&-13&-19\\3&16&7&-13\end{bmatrix}\\&Tr(A)=(20)+(8)+(-13)+(-13)=2\end{align*}$

$\displaystyle \begin{align*}&\text{Tr, that is to say the trace, of a square nxn matrix is the its diagonal elements:}\\&\text{i.e. }Tr\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}=a+e+i\\&\text{For the matrix }A=\begin{bmatrix}-3&-1&-16\\4&-11&-5\\3&-10&-9\end{bmatrix}\\&\text{We find: }\\&Tr(A)=(-3)+(-11)+(-9)=-23\end{align*}$

$\displaystyle \begin{align*}&\text{The trace of a square nxn matrix is the sum of its diagonal elements:}\\&\sum_{i=1}^{n}A_{i,i}\\&\text{For the matrix }\begin{bmatrix}3&-16&17&16\\13&-10&4&-20\\-3&-8&-14&-13\\-3&-17&4&-1\end{bmatrix}\\&\text{This becomes: }\\&(3)+(-10)+(-14)+(-1)=-22\end{align*}$