Complete the following figure matrix.

The correct answer is the first option.

By analyzing the grid row by row, we can identify a consistent pattern of shading regions:

1. Row 1 Analysis:
- The first figure consists of a large triangle divided into 4 smaller, unshaded triangles.
- The second figure has 1 region shaded (the top triangle).
- The third figure has 2 regions shaded (the top triangle and the central inverted triangle).

2. Row 2 Analysis:
- The first figure consists of a circle divided into 4 unshaded quadrants.
- The second figure has 1 region shaded (the top-right quadrant).
- The third figure has 2 regions shaded (the top-right and bottom-right quadrants, forming the right half).

3. Row 3 Analysis:
- The first figure consists of a rectangle divided into 4 unshaded triangular regions by its diagonals.
- The second figure has 1 region shaded (the top triangle).
- Following the established pattern, the missing third figure must have 2 regions shaded (the top and the right triangles).

Boundary Line Logic:
- Since both the top and right triangular regions are shaded with the same horizontal pattern, they merge. The boundary line separating them (the segment from the center to the top-right corner) becomes absorbed into the shading and is no longer drawn.
- The two remaining unshaded regions (the left and bottom triangles) must still be separated, so the boundary line between them (the segment from the bottom-left corner to the center) remains visible.
- The diagonal dividing the shaded top-right half from the unshaded bottom-left half (running from the top-left to the bottom-right corner) also remains fully visible.

This combination of lines and shading corresponds exactly to the first option.