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.

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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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Which of the following sets forms a basis for the vector space given by the plane? — 26х — 32у — 282 %3D 0 {(:)(} "{()} {(:)( {( -2 2 I. -5 5 -26 II. -32 -28 16 III. -6 -8 -2 6 IV. -5 А. II., IV. only В. П, II, only. C. None of the above. D. I, III, only. Е. I, II, only.
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just b)
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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.