Question

Find the values of the variables. [Start 2 By 3 Matrix 1st Row 1st Column a plus 7 2nd Column 2 z plus 1 3rd Column 3 m 2nd Row 1st Column 6 k 2nd Column 5 3rd Column 1 EndMatrix ]plus[Start 2 By 3 Matrix 1st Row 1st Column 12 a 2nd Column 6 z 3rd Column 5 m 2nd Row 1st Column 7 k 2nd Column 4 3rd Column 2 EndMatrix ]equals[Start 2 By 3 Matrix 1st Row 1st Column 33 2nd Column negative 39 3rd Column 32 2nd Row 1st Column 39 2nd Column 9 3rd Column 3 EndMatrix ]

Answer 1

Answer:

a=2, z= 4.75, m=4, k=3

Step-by-step explanation:

$\begin{equation*} \begin{pmatrix}a+7 & 2z+1 & 3m \\6k & 5 & 1\end{pmatrix} + \begin{pmatrix}12a & 6z & 5m \\7k & 4 & 2\end{pmatrix} = \begin{pmatrix}33 & 39 & 32 \\39 & 9 & 3\end{pmatrix} \end{equation*}$

In Matrix Addition, each element in corresponding position is added.

In Matrix Equality, elements in the same position are equal.

Applying these two principles

a+7+12a=33

13a=33-7

13a=26

a=2

2z+1+6z=39

8z=39-1

8z=38

z= 4.75

3m+5m=32

8m=32

m=4

6k+7k=39

13k=39

k=3

Therefore:

a=2, z= 4.75, m=4, k=3