Let X₁ be a closed subspace and X₂ be a finite dimensional subspace of a normed space X. Prove that X₁ + X₂ is closed in X.
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- Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 37. V = P, W is the set of all polynomials of degree 3
- In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[a0a]}In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba]}In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn, W is the set of diagonal nn matrices