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

[tex] \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} [/tex]

Answer:

m = 45

n = 12

kudzordzifrancis kudzordzifrancis · Answer 2 · 2019-02-02T18:12:30+01:00

Answer:

The correct answer is B

[tex]m=45[/tex]

[tex]n=12[/tex]

Step-by-step explanation:

The given matrix equation is:

[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 add the corresponding entries on the left hand side to obtain;

[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]

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

We now equate the corresponding entries to obtain;

[tex]n-2=10[/tex]

[tex]\Rightarrow n=10+2[/tex]

[tex]\Rightarrow n=12[/tex]

Also;

[tex]m-5=40[/tex]

[tex]\Rightarrow m=40+5[/tex]

[tex]\Rightarrow m=45[/tex]