Math  /  Algebra

Question2. Show that the sets consisting of vectors of the following form are subspaces of R3\mathbf{R}^{3} or R4\mathbf{R}^{4}. (c) (a,2a,a)(a, 2 a,-a)

Studdy Solution
Check if the set is closed under scalar multiplication:
Take an arbitrary vector from the set, (a,2a,a)(a, 2a, -a), and a scalar cc. Multiply the vector by the scalar:
c(a,2a,a)=(ca,2ca,ca) c(a, 2a, -a) = (ca, 2ca, -ca)
Let a=ca a' = ca . The resulting vector (a,2a,a)(a', 2a', -a') is in the set, so the set is closed under scalar multiplication.
Since all three conditions are satisfied, the set of vectors (a,2a,a)(a, 2a, -a) is a subspace of R3\mathbf{R}^3.

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