Yes, parentheses are important when working with matrices. It helps to clearly define the operations and ensure that they are applied correctly. Since you didn't mention any parentheses in your question, I'll assume that the matrices are written without them.
To solve this problem, we need to find the values of the variables (a, z, m, k) in each equation. We can do this by simplifying the equations using matrix operations.
Let's start by adding the matrices on both sides of the equation. Remember that when adding matrices, you add the corresponding elements together.
Matrix 1 + Matrix 2 = Matrix 3
(a + 2) + (3a) = 10
(3z + 1) + (2z) = -14
(5m) + (5m) = 80
(4k) + (2k) = 10
(0) + (5) = 5
(3) + (6) = 9
Now we can simplify these equations further:
4a = 10 - 2
5z = -14 - 1
10m = 80/2
6k = 10/2
5 = 5
9 = 9
Now, let's solve for each variable:
a = (10 - 2)/4
z = (-14 - 1)/5
m = 80/20
k = 10/6
Simplifying these equations will give us the values of the variables:
a = 8/4 = 2
z = -15/5 = -3
m = 4
k = 5/3
Therefore, the values of the variables are:
a = 2
z = -3
m = 4
k = 5/3
Remember to always double-check your calculations and be careful with signs when working with matrix operations.