Question

Which of the following statements best explains why the transformation \( T \) from \( \mathbb{R}^3 \) to \( \mathbb{R}^6 \) is not a rigid transformation of \( \mathbb{R}^3 \)?

A) The dimensions of the codomain \( \mathbb{R}^6 \) differ from the domain \( \mathbb{R}^3 \).
B) The transformation matrix \( T \) is not invertible.
C) The determinant of the transformation matrix \( T \) is zero.
D) The transformation \( T \) preserves the Euclidean distance but not the angle between vectors in \( \mathbb{R}^3 \).

Answer 1

The transformation T from R³ to R⁶ is not a rigid transformation because it does not preserve the angle between vectors in R³.

Step-by-step explanation:

The correct answer is D) The transformation T preserves the Euclidean distance but not the angle between vectors in R³.

A rigid transformation is a transformation that preserves distance and angle. In other words, if a transformation is rigid, the distance between any two points will remain the same, and the angle between any two vectors will remain the same. However, in this case, the transformation T only preserves the distance between points in R³, but it does not preserve the angle between vectors. Therefore, it is not a rigid transformation.