ANSWER
The correct answer is [tex]m=45,n=12[/tex].
EXPLANATION
We were given the matrix equation;
[tex]\left[\begin{array}{cc}n-1&6\\-19&m+3\end{array}\right] +\left[\begin{array}{cc}-1&0\\16&-8\end{array}\right] =\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].
We must first simplify the Left Hand Side of the equation by adding corresponding entries.
[tex]\left[\begin{array}{cc}n-1+-1&6+0\\-19+16&m+3-8\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].
That is;
[tex]\left[\begin{array}{cc}n-2&6\\-3&m-5\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].
Since the two matrices are equal, their corresponding entries are also equal. we equate corresponding entries and solve for m and n.
This implies that;
[tex]n-2=10[/tex]
We got this equation from row one-column one entry of both matrices.
[tex]n=12[/tex]
Also, the row three-column three entries of both matrices will give us the equation;
[tex]m-5=40[/tex]
[tex]m=45[/tex]
Hence the correct answer is [tex]m=45,n=12[/tex].
The correct option is option 2
