(a) (b) (c) Let U be the subspace of R defined by U = {(X1, X2,...

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(a) (b) (c) Let U be the subspace of R³ defined by U = {(X1, X2, X3, X4, X5) € R³ : x₁ = 3x₂ and x3 = 7x4}. Find a basis of U. Extend the basis in part (a) to a basis of R5. Find a subspace W of R5 such that R5 = U @ W. (a) (b) (c) Let U be the subspace of R³ defined by U = {(X1, X2, X3, X4, X5) € R³ : x₁ = 3x₂ and x3 = 7x4}. Find a basis of U. Extend the basis in part (a) to a basis of R5. Find a subspace W of R5 such that R5 = U @ W.

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The detailed answer for the above question is provided below a To find a basis of U we can use the f... View the full answer