To solve the problem, we need to establish the relationships between the given arrays and the values they represent.

1. Understanding the Arrays:

   • The first array is a 3x3 matrix formed from the numbers: 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}$$
   • The second array is a 2x3 matrix formed from: -10 & 60 & 20 \\ -50 & -40 & a \end{bmatrix}$$

2. Substituting $a$: Given $a = -150$, the second matrix becomes:

   -10 & 60 & 20 \\ -50 & -40 & -150 \end{bmatrix}$$

3. Forming the Output Array: The problem states that these matrices result in an output array represented by $[u, v, w, x, y, z]$. Since there isn't a specific operation defined between these matrices, let's assume we concatenate them or perform an operation that combines the matrices row-wise or column-wise.

4. Determining the Values:

   • If we concatenate these matrices, we could write: [ [u, v, w, x, y, z] = [1, 2, 3, 4, 5, 6, 7, 8, 9, -10, 60, 20, -50, -40, -150] ] The output would then contain all values from both matrices.

5. Finding $z$: Since $z$ is the last element in this concatenated array, we identify it as:
   $z = -150$

Thus, the value of $z$ is $-150$.

Summary

The value of $z$ is $-150$.

Would you like more details on this calculation or have any questions? Here are some related questions you might consider:

1. What are the operations that can combine matrices?
2. How do you derive values from matrix multiplication?
3. Can you provide examples of matrix concatenation?
4. What are the dimensions of the resulting matrix after certain operations?
5. How would the result change if $a$ had a different value?

Tip: Always define the operation between matrices clearly to avoid ambiguity in the result.