Q1Multiple correct6 Marks10 May 2026

Choose all the subspaces isomorphic to $\mathbb{R}^3$ from the options given below.

A

W1 = { $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ in v_2x2}(R) : a = 0 }

B

W2 = { $(x, y, z, w)$ in $\mathbb{R}^4$ : x - y = z, w = x }

C

W3 = { $\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}$ in v_3x3}(R) : a+d+g=0, b-e+h=0, c+f+i=0 }

D

W4 = { $(x, y, z)$ in $\mathbb{R}^3$ : $(x, y, z)$ is orthogonal to $(0,0,0)$ with respect to the standard dot product in $\mathbb{R}^3$ }