Let WWW be the set of all (x1,x2,x3,x4,x5)∈R5(x_1, x_2, x_3, x_4, x_5) \in \mathbb{R}^5(x1,x2,x3,x4,x5)∈R5 satisfying all three of the following:
x1+x2−x3+2x4+x5=0x_1 + x_2 - x_3 + 2x_4 \phantom{{}+x_5} = 0x1+x2−x3+2x4+x5=0 2x1+2x2−x3+5x4+x5=02x_1 + 2x_2 - x_3 + 5x_4 + x_5 = 02x1+2x2−x3+5x4+x5=0 3x1+3x2−2x3+7x4+x5=03x_1 + 3x_2 - 2x_3 + 7x_4 + x_5 = 03x1+3x2−2x3+7x4+x5=0
Being the solution set of a homogeneous system, WWW is a subspace of R5\mathbb{R}^5R5.
What is dimW\dim WdimW?
Select all that apply.
333
222
444
111