(a) If U and V are vector subspaces of Rn, then U ∪ V is also a vector subspace of Rn.   (b) If V and W are vector spaces of the same dimension, n, and T : V → W is any linear transformation, then it is always possible to choose bases α, of V, and β, of W, such that the matrix of T with respect to to these bases is the n×n identity matrix.   (c) Let u = (2, 0, −1), v = (3, 1, 0), and w = (c, −2, 2), where c ∈ R. The set {u,v,w} is a basis of R3 only if c ≠ −7.

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A: Here we can use the composition of function formula to find the required values.

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A: Linear algebra

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A: We simply use the the defination of matrix representation of linear transformation .

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A: Here we can use the composition of function formula to find the required values.

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Q: 2. Decide if the following statement is True or False: Let V be a vector space, and let T: V R be a…

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A: The solution is given below

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