Given the matrix equation:

Equating the corresponding elements, we get two equations:

1. \(2x - 1 = x + 3\)
2. \(3x = 12\)
3. \(y^2 - 1 = 35\)

Solving for \(x\) from equation (1) or (2):

From equation (1): \(2x - 1 = x + 3 \Rightarrow x = 4\)

From equation (2): \(3x = 12 \Rightarrow x = 4\)

So, \(x = 4\)

Solving for \(y\) from equation (3):

\(y^2 - 1 = 35 \Rightarrow y^2 = 36 \Rightarrow y = \pm 6\)

So, \(y = 6\) or \(y = -6\)

Now, we need to find the value of \(x - y\):

If \(y = 6\), then \(x - y = 4 - 6 = -2\)

If \(y = -6\), then \(x - y = 4 - (-6) = 4 + 6 = 10\)

Therefore, the value of \(x - y\) is either \(-2\) or \(10\).