1. The problem is to find the determinant of the given 3x3 matrix: $$\begin{vmatrix} 1 & 1 & 0 \\ 7z & 2x & 0 \\ x & y & 2 \end{vmatrix}$$ 2. Note that the top row appears incomplete as two elements (1,1) are provided but a 3x3 matrix requires three elements in each row. The same applies for the second row (7z, 2x) and the third row (x, y, 2). 3. Based on the user's input, it seems the matrix might be: $$\begin{bmatrix} 1 & 1 & 0 \\ 7z & 2x & 0 \\ x & y & 2 \end{bmatrix}$$ where we've inferred the top row's third element and the second row's third element to be 0 to complete a 3x3 matrix. 4. The determinant of a 3x3 matrix $$\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}$$ is: $$a(ei - fh) - b(di - fg) + c(dh - eg)$$ 5. Substitute the matrix elements: $$a=1, b=1, c=0, d=7z, e=2x, f=0, g=x, h=y, i=2$$ 6. Calculate each component: $$ei - fh = (2x)(2) - (0)(y) = 4x - 0 = 4x$$ $$di - fg = (7z)(2) - (0)(x) = 14z - 0 = 14z$$ $$dh - eg = (7z)(y) - (2x)(x) = 7zy - 2x^2$$ 7. Calculate determinant: $$1 \cdot 4x - 1 \cdot 14z + 0 \cdot (7zy - 2x^2) = 4x - 14z + 0 = 4x - 14z$$ 8. Thus, the determinant of the matrix is: $$\boxed{4x - 14z}$$