You are right. The original notation was not precise enough.
[R|t]X is valid only when X is written as a homogeneous 3D point, i.e., X_bar = [X; 1], which is a 4-dimensional vector. If X denotes the 3D point in R^3, then the correct form is RX + t.
So your dimensionality concern is correct. The original solution mixed the point X in R^3 and the homogeneous point X_bar in R^4. We have updated the notation in the answer file and re-uploaded the Exam 2025 Answer file.
[R|t]X is valid only when X is written as a homogeneous 3D point, i.e., X_bar = [X; 1], which is a 4-dimensional vector. If X denotes the 3D point in R^3, then the correct form is RX + t.
So your dimensionality concern is correct. The original solution mixed the point X in R^3 and the homogeneous point X_bar in R^4. We have updated the notation in the answer file and re-uploaded the Exam 2025 Answer file.
