Determine the dimension, Consider two subspaces U1 and U2,

Determine the dimension

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Reference no: EM132354412

Question 1 - Which of the following sets are subspaces of R³?

a. A = {(λ, λ + μ³, λ - μ³)| λ, μ ∈ R}

b. B = {λ², - λ², 0)| λ ∈ R}

c. Let γ be in R.

C = {(ξ₁, ξ₂, ξ₃) ∈ R³|ξ₁ - 2ξ₂ + 3ξ₃ = γ}

d. D = {(ξ₁, ξ₂, ξ₃) ∈ R³|ξ₂ ∈ Z}

Question 2 - Consider two subspaces U₁ and U₂, where U₁ is the solution space of the homogeneous equation system A₁x = 0 and U₂ is the solution space of the homogeneous equation system A₂x = 0 with

a. Determine the dimension of U₁, U₂.

b. Determine bases of U₁ and U₂.

c. Determine a basis of U₁ ∩ U₂.

Reference no: EM132354412

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