Q3Multiple correct7 Marks10 May 2026

Choose all the subspaces isomorphic to $\mathbb{R}^3$.

A

W1 = { $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ in v_2x2}(R) : a + b - c = 0, c + d = 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 is the column space of the matrix $\begin{bmatrix} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end{bmatrix}$

E

W5 = { $(x, y, z)$ in $\mathbb{R}^3$ : $(x, y, z)$ is orthogonal to the zero vector in $\mathbb{R}^3$ with respect to the standard dot product }