The matrices shown below must be equal to each other. \[ \left[\begin{array}{cc}x & 2 y \\ z & 9\end{array}\right]=\left[\begin{array}{cc}4 & 12 \\ 3 & 9\end{array}\right] \] Find the value of each variable and enter it in the relevant box provided below: \( \boldsymbol{x}=\square \) \( \boldsymbol{z}= \)

To solve for the variables \(x\), \(y\), and \(z\) from the equation of matrices, we equate the corresponding elements. 1. From the top-left corner: \(x = 4\). 2. From the top-right corner: \(2y = 12\) which gives \(y = 6\). 3. From the bottom-left corner: \(z = 3\). 4. The bottom-right corner confirms our work since both are equal to 9. Thus, the values for the variables are: \( \boldsymbol{x}=4 \) \( \boldsymbol{z}=3 \)