what about if it was -24

You are asking what the result would be if the first element of the resulting matrix was -24 instead of 24. However, the calculation for the first element, $c_{1,1}$, is fixed by the given matrices $A$ and $x$.

Let's re-evaluate the calculation for $c_{1,1}$ to ensure accuracy. $c_{1,1} = (6)(4) + (2)(-2) + (4)(1)$ $c_{1,1} = 24 - 4 + 4$ $c_{1,1} = 20 + 4$ $c_{1,1} = 24$

The calculation shows that $c_{1,1}$ is indeed 24. If the problem statement or the matrix $A$ or $x$ were different, then $c_{1,1}$ could be -24.

For example, if the first row of matrix $A$ was $\begin{bmatrix} -6 & 2 & 4 \end{bmatrix}$ and $x$ remained the same, then: $c_{1,1} = (-6)(4) + (2)(-2) + (4)(1)$ $c_{1,1} = -24 - 4 + 4$ $c_{1,1} = -28 + 4$ $c_{1,1} = -24$ In this hypothetical scenario, the first element would be -24.

However, based on the original matrices provided in the image: $A = \begin{bmatrix} 6 & 2 & 4 \\ -1 & 4 & 3 \\ -2 & 9 & 3 \end{bmatrix}$ $x = \begin{bmatrix} 4 \\ -2 \\ 1 \end{bmatrix}$ The correct calculation for the first element is $c_{1,1} = 24$.

Therefore, the original answer remains correct: Ax = \begin{bmatrix 24 \\ -9 \\ -23 \end{bmatrix}}