Question

What are the values of m and n in the matrix addition below?

Answer 1

The correct answer is
`m=45,n=12`.

Step-by-step explanation

We were given the matrix equation;

`\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]`.

We must first simplify the Left Hand Side of the equation by adding corresponding entries.

`\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]`.

That is;

`\left[\begin{array}{cc}n-2&6\\-3&m-5\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right]`.

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;

`n-2=10`

We got this equation from row one-column one entry of both matrices.

`n=12`

Also, the row three-column three entries of both matrices will give us the equation;

`m-5=40`

`m=45`

Hence the correct answer is
`m=45,n=12`.

The correct option is option 2