2) Find the value of \( x, y \) and \( z \). \( \left(\begin{array}{c}x \\ x-10 \\ 2 y-2\end{array}\right)=\left(\begin{array}{l}6 \\ y \\ z\end{array}\right) \)

To find the values of \( x \), \( y \), and \( z \), we can set up a system of equations based on the given vector equation: \[ \left(\begin{array}{c}x \\ x-10 \\ 2y-2\end{array}\right) = \left(\begin{array}{l}6 \\ y \\ z\end{array}\right) \] This gives us the following equations: 1. From the first component: \[ x = 6 \] 2. From the second component: \[ x - 10 = y \] 3. From the third component: \[ 2y - 2 = z \] Now, we can substitute \( x = 6 \) into the second equation to find \( y \): \[ 6 - 10 = y \implies y = -4 \] Next, we substitute \( y = -4 \) into the third equation to find \( z \): \[ 2(-4) - 2 = z \implies -8 - 2 = z \implies z = -10 \] Thus, we have found the values: \[ x = 6, \quad y = -4, \quad z = -10 \] In conclusion, the values are: \[ \boxed{(6, -4, -10)} \]