Q24Multiple correct2 Marks3 Sep 2023

Let U = {(x, y, z) in $\mathbb{R}^3$ : x = y = z} and V = {(x, y, z) in $\mathbb{R}^3$ : x + y + z = 0}. Let 1_{U} and 1_{V} be the projections on the spaces U and V respectively. Which of the following statement(s) is/are true?

A

{(-1, 1, 0), (-1, -1, 2)} is a basis for the range space of 1_{U}.

B

{(-1, 1, 0), (-1, -1, 2)} is a basis for the null space of 1_{U}.

C

{(1, 1, 1)} is a basis for the range space of 1_{V}.

D

{(1, 1, 1)} is a basis for the null space of 1_{V}.