Q11Comprehension5 Marks3 Aug 2025PassageLet T:R3→R3T:\mathbb{R}^3\to\mathbb{R}^3T:R3→R3 be the linear transformation defined by T(x,y,z)=(x+z, y, x+y+z)T(x,y,z)=(x+z,\ y,\ x+y+z)T(x,y,z)=(x+z, y, x+y+z) for all (x,y,z)∈R3(x,y,z)\in\mathbb{R}^3(x,y,z)∈R3.Which of the following spaces are isomorphic to the kernel of TTT?AThe trivial vector space {0}\{0\}{0}.BThe vector space of 2×22\times22×2 diagonal matrices.CThe yzyzyz-plane in R3\mathbb{R}^3R3, i.e., {(0,y,z)∣y,z∈R}\{(0,y,z)\mid y,z\in\mathbb{R}\}{(0,y,z)∣y,z∈R}.DThe vector space of 2×22\times22×2 scalar matrices.EThe space of solutions to Ax=0Ax=0Ax=0, where AAA is an invertible matrix.FThe xxx-axis in R3\mathbb{R}^3R3, i.e., {(x,0,0)∣x∈R}\{(x,0,0)\mid x\in\mathbb{R}\}{(x,0,0)∣x∈R}.
