Transformation T:R^(3) → R^(2)
- The transformation T is defined as T(x, y, z) = (x, 1, y, z).
- This means that T takes a vector in R^(3) (three-dimensional space) and maps it to a vector in R^(2) (two-dimensional space).
- The transformation simply discards the second and third components of the input vector and retains the first component as the first component of the output vector. The second component of the output vector is always 1.

Transformation S:R^(3) → R^(2)
- The transformation S is defined as S(x, y, z) = (|x|, 0).
- This transformation takes a vector in R^(3) and maps it to a vector in R^(2).
- The absolute value of the first component of the input vector becomes the first component of the output vector, and the second component of the output vector is always 0.
- This transformation effectively reflects the first component of the input vector across the y-axis and sets the second component to 0.

Explanation
- Transformation T simply removes the second and third components of the input vector and keeps the first component as the first component of the output vector.
- Transformation S reflects the first component of the input vector across the y-axis and sets the second component to 0 in the output vector.
- Both transformations result in a reduction in dimensionality from R^(3) to R^(2), but they achieve this in different ways.
- Transformation T keeps the first component of the input vector unchanged, while transformation S modifies the first component by taking its absolute value.