Let α = (A 1, A2, A3), β = (B 1, B2, B3) ∈ u and any λ, μ∈R, and prove that λα+μβ∈U is the subspace of R3. The concrete steps are as follows: take α = (A 1, A2, A3), β = (B 1, B2, B3) ∈ U and any λ, μ ∈ R., then λ α+μ β = (λ a1+μ b.

Mathematics [English: Mathematics, derived from the ancient Greek μ θ η μ α (má th ē ma); Often abbreviated as math or maths], it is a discipline that studies concepts such as quantity, structure, change, space and information.

Mathematics is a universal means for human beings to strictly describe the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence. In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.