- #1
Mr Davis 97
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Homework Statement
##W_1 = \{(a_1, a_2, a_3) \in \mathbb{R}^3 : a_1 = 3a_3,~ a_3 = -a_2 \}##
##W_2 = \{(a_1, a_2, a_3) \in \mathbb{R}^3 : 2a_1 - 7a_2 + a_3 = 0 \}##
Given that these are two subspaces of ##\mathbb{R}^3##, describe the intersection of the two, i.e. ##W_1 \cap W_2## and show that it is a subspace.
Homework Equations
The Attempt at a Solution
Would it be sufficient just to say that ##W_1 \cap W_2 = \{(a_1, a_2, a_3) \in \mathbb{R}^3 : 2a_1 - 7a_2 + a_3 = 0,~a_1 = 3a_3,~ a_3 = -a_2 \}## and proceed to show that it is a subspace?