Question

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

Answer 1

`\left[\begin{array}{ccc}n-1&6\\-19&m+3\end{array}\right] +\left[\begin{array}{ccc}-1&0\\16&-8\end{array}\right] =\left[\begin{array}{ccc}10&6\\-3&40\end{array}\right]\\\left[\begin{array}{ccc}n-1+(-1)&6+0\\-19+16&m+3+(-8)\end{array}\right] =\left[\begin{array}{ccc}10&6\\-3&40\end{array}\right]\\\left[\begin{array}{ccc}n-2&6\\-3&m-5\end{array}\right] =\left[\begin{array}{ccc}10&6\\-3&40\end{array}\right]\\\Downarrow\\n-2=10\ \wedge\ m-5=40\\\boxed{n=12\ \wedge\ m=45}`

Answer:

m = 45

n = 12

Answer 2

The correct answer is B

`m=45`

`n=12`

Explanation:

The given matrix equation is:

`\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 add the corresponding entries on the left hand side to obtain;

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

The above two matrices are equal. This means that, their corresponding entries are equal.

We now equate the corresponding entries to obtain;

`n-2=10`

`\Rightarrow n=10+2`

`\Rightarrow n=12`

Also;

`m-5=40`

`\Rightarrow m=40+5`

`\Rightarrow m=45`