Solved GATE DA 2024 Question Paper | DETAILED VIDEO SOLUTIONS | DA & AI | Q. 49 Projection Matrix
Q.49 Let ℝ be the set of real numbers, 𝑈 be a subspace of ℝ
3
and 𝑴 ∈ ℝ
3×3 be the
matrix corresponding to the projection on to the subspace 𝑈.
Which of the following statements is/are TRUE?
(A)
If 𝑈 is a 1-dimensional subspace of ℝ
3
, then the null space of 𝑴 is a
1-dimensional subspace.
(B) If 𝑈 is a 2-dimensional subspace of ℝ
3
, then the null space of 𝑴 is a
1-dimensional subspace.
(C) 𝑴2 = 𝑴
(D) 𝑴3 = �
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