17. Find a basis for the subspace of R³ that is spanned by the vectors v₁ = (1, 0, 0), V₂ = (1,0,1), V3 = (2,0,1), V₁ =
Posted: Mon Jul 11, 2022 12:44 pm
- 17 Find A Basis For The Subspace Of R That Is Spanned By The Vectors V 1 0 0 V 1 0 1 V3 2 0 1 V 1 (9.89 KiB) Viewed 24 times
- 17 Find A Basis For The Subspace Of R That Is Spanned By The Vectors V 1 0 0 V 1 0 1 V3 2 0 1 V 2 (26.33 KiB) Viewed 24 times
- 17 Find A Basis For The Subspace Of R That Is Spanned By The Vectors V 1 0 0 V 1 0 1 V3 2 0 1 V 3 (18.67 KiB) Viewed 24 times
17. Find a basis for the subspace of R³ that is spanned by the vectors v₁ = (1, 0, 0), V₂ = (1,0,1), V3 = (2,0,1), V₁ = (0, 0, -1)
21. a. Prove that for every positive integer n, one can find n + 1 linearly independent vectors in F(-∞, ∞). [Hint: Look for polynomials.] b. Use the result in part (a) to prove that F(-∞, ∞) is infinite- dimensional. c. Prove that C(-∞, ∞), Cm(-∞, ∞), and C∞ (-∞, ∞o) are infinite-dimensional.
22. Let S be a basis for an n-dimensional vector space V. Prove that if V₁, V₂, ..., V, form a linearly independent set of vectors in V, then the coordinate vectors (v₁)s, (V₂)s,..., (vr)s form a linearly independent set in R", and conversely.