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: \( x= \) \( y= \) \( z= \)

To find the values of \( x \), \( y \), and \( z \), we can set the corresponding elements of the two matrices equal to each other: 1. The first element: \( x = 4 \) 2. The second element: \( 2y = 12 \) → Dividing both sides by 2 gives \( y = 6 \) 3. The third element: \( z = 3 \) 4. The fourth element: \( 9 = 9 \) is already satisfied. Now, we have the values: \( x = 4 \) \( y = 6 \) \( z = 3 \)