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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.

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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 22EQ
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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.
Transcribed Image Text: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.
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