Let ℝ be the set of real numbers, 𝑈 be a subspace of ℝ³ and 𝑴 ∈ ℝ³×³ be the…
Let ℝ be the set of real numbers, 𝑈 be a subspace of ℝ³ and 𝑴 ∈ ℝ³×³ be the matrix corresponding to the projection onto the subspace 𝑈. Which of the following statements is/are TRUE?
- A.
If 𝑈 is a 1-dimensional subspace of ℝ³, then the null space of 𝑴 is a 1-dimensional subspace.
- B.
If 𝑈 is a 2-dimensional subspace of ℝ³, then the null space of 𝑴 is a 1-dimensional subspace.
- C.
𝑴² = 𝑴
- D.
𝑴³ = 𝑴
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