What is the matrix transformation which takes independent vectors [1, 2] and [2, 5] and transforms them to [1, 1] and [3, 2] respectively?
- A. [[1, 1], [1, 0]]
- B. [[0, 0], [0.5, 0.5]]
- C. [[-1, 0], [1, 1]]
- D. [[-1, 1], [1, 0]]
Answer: D. [[-1, 1], [1, 0]]
Explanation: Let matrix be M. M [1, 2]^T = [1, 1]^T and M [2, 5]^T = [3, 2]^T. M [[1, 2], [2, 5]] = [[1, 3], [1, 2]]. M = [[1, 3], [1, 2]] * inv([[1, 2], [2, 5]]). Det = 5-4=1. Inv = [[5, -2], [-2, 1]]. M = [[1, 3], [1, 2]] * [[5, -2], [-2, 1]] = [[-1, 1], [1, 0]].