SOLUTION: Consider the vector space ℝ3 and its subset 𝑆 𝑆 = {(𝑎, 𝑏, 𝑐) ∶ 3𝑎 − 4𝑏 + 𝑐 = 0, 𝑎 + 2𝑏 − 𝑐 = 0, 𝑎, 𝑏, 𝑐 ∈ ℝ} Show that 𝑆

Question 1182334: Consider the vector space ℝ3
and its subset 𝑆
𝑆 = {(𝑎, 𝑏, 𝑐) ∶ 3𝑎 − 4𝑏 + 𝑐 = 0, 𝑎 + 2𝑏 − 𝑐 = 0, 𝑎, 𝑏, 𝑐 ∈ ℝ}
Show that 𝑆 is a subset of ℝ3
and also find dim 𝑆 .
Determine whether or not the vectors (1, −3,2), (2,4,1) and (1,1,1) form a basis of ℝ3
Are the following sets linearly independent or linearly dependent?
𝐴 = {(3 − 𝑖, 2 + 2𝑖, 4), (2,2 + 4𝑖, 3), (1 − 𝑖, −2𝑖, 1)} ; 𝐵 = {(1,2,3), (1,3,2), (3,7,8)}
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
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