4. Let U be a subspace of a finite dimensional F-vector space V with dim U = k anddim V = n. Prove that if By = (.....) is a basis for U and By = (U₁₁ U₁₁ U₁+1U₂)is a basis for V. thenBy/U = (k+1+U₂+U}is a basis for V/U.

Answered: Image /qna-images/answer/daa3ef6d-4d04-4915-824f-8cd4920ab196.jpg

Answered: 4. Let U be a subspace of a finite…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Let U be a subspace of a finite dimensional F-vector space V with dim U = k and dim V = n. Prove that if By = (.....) is a basis for U and By = (U₁₁ U₁₁ U₁+1U₂) is a basis for V. then By/U = (k+1+U₂+U} is a basis for V/U.