Q23Comprehension2 Marks30 Apr 2023PassageConsider the subspace W = { (x,y,z)(x, y, z)(x,y,z) | x - y + z = 0, x, y, z in R } of R3\mathbb{R}^3R3. Answer the given subquestions based on the given information.Which of the following is a basis β\betaβ for W?Aβ\betaβ = { (1,1,0)(1, 1, 0)(1,1,0), (−1,0,1)(-1, 0, 1)(−1,0,1) }Bβ\betaβ = { (1,1,0)(1, 1, 0)(1,1,0), (0,1,−1)(0, 1, -1)(0,1,−1) }Cβ\betaβ = { (0,1,1)(0, 1, 1)(0,1,1), (1,1,0)(1, 1, 0)(1,1,0), (−1,0,1)(-1, 0, 1)(−1,0,1) }Dβ\betaβ = { (0,1,1)(0, 1, 1)(0,1,1), (0,1,−1)(0, 1, -1)(0,1,−1) }
