Exercise 1.9 Consider the following subspaces of R³: V₁ V₂ = ((1,0, 1, 1, 0), (-1, 1, 0, 0, 1), (0, 0, 0, 1, -1)) ((0, 1, 1, 1, 1), (1, 1, 2, 2, 1), (1, 0, 1, 1, 1)) a) Determine a basis B₁ of V₁ and a basis B₂ of V₂. Compute dim(V₁) and dim(V₂). b) Determine a basis of V₁ V₂ and one of V₁ + V₂. Compute dim(V₁V₂) and dim(V₁+V₂). Are the subspaces V₁ and V₂ in direct sum? c) Write if possible the vector v = (1,0, 1, 1, 0) as a sum v = V₁ + V₂ with v₁ € V₁, V2 € V₂ and v₁ (0,0,0,0,0) and v2 # (0, 0, 0, 0, 0). Is the expression unique?

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