Match List with List II. List gives matrices representing transformations

Solution overview: Identify each 3×3 homogeneous matrix by its effect on 2D coordinates, then match it to the appropriate diagram.

• Matrix [2 0 0; 0 2 0; 0 0 1] → uniform scale by factor 2. Diagonal entries (2,2) scale x and y; this matches the scale diagram (scale (2,2)).

• Matrix [1 0 2; 0 1 2; 0 0 1] → translation by (2, 2). The last column (2,2) gives the translation vector; this matches the translate diagram (translate (2,2)).

• Matrix [0.5 -0.866 0; 0.866 0.5 0; 0 0 1] → rotation by 60°. Entries match cos60° = 0.5 and sin60° ≈ 0.866, so it is a rotation matrix; this matches the rotate(60°) diagram.

• Matrix [1 2 0; 0 1 0; 0 0 1] → horizontal shear (x' = x + 2y). The off-diagonal 2 in the top-right produces a shear in the x-direction; this matches the shear diagram.

Final matching (matrix → diagram): [2 0 0; 0 2 0; 0 0 1] → scale, [1 0 2; 0 1 2; 0 0 1] → translate (2,2), [0.5 -0.866 0; 0.866 0.5 0; 0 0 1] → rotate 60°, [1 2 0; 0 1 0; 0 0 1] → shear.