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Q1 () 1 U2 = uj 2 Given are the vectors and Span{v1, v2} a) Determine if these vectors are in the linear envelope of the vectors V, = ) and V,-(3) If possible, also express the vectors u1, u2 as linear combinations of v1 and v2. b) Justify if it is possible to express the vectors u1 and u2 as linear combinations of v1 and v2 in more ways than one. c) Also explain the relevance (regarding existence and unambiguity) of the answers in (a) and (b) for the question of solubility to the equations Ax = ul and Ax = u2 if A is the matrix with columns given by v1 and v2.

Q1 () 1 U2 = uj 2 Given are the vectors and Span{v1, v2} a) Determine if these vectors are in the linear envelope of the vectors V, = ) and V,-(3) If possible, also express the vectors u1, u2 as linear combinations of v1 and v2. b) Justify if it is possible to express the vectors u1 and u2 as linear combinations of v1 and v2 in more ways than one. c) Also explain the relevance (regarding existence and unambiguity) of the answers in (a) and (b) for the question of solubility to the equations Ax = ul and Ax = u2 if A is the matrix with columns given by v1 and v2.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 21EQ
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Q1 1 u2 uj 2 Given are the vectors and Span{v1, v2} a) Determine if these vectors are in the linear envelope of the vectors V, = ) and V,-(3) If possible, also express the vectors u1, u2 as linear combinations of v1 and v2. b) Justify if it is possible to express the vectors u1 and u2 as linear combinations of v1 and v2 in more ways than one. c) Also explain the relevance (regarding existence and unambiguity) of the answers in (a) and (b) for the question of solubility to the equations Ax = ul and Ax = u2 if A is the matrix with columns given by v1 and v2.
Transcribed Image Text:Q1 1 u2 uj 2 Given are the vectors and Span{v1, v2} a) Determine if these vectors are in the linear envelope of the vectors V, = ) and V,-(3) If possible, also express the vectors u1, u2 as linear combinations of v1 and v2. b) Justify if it is possible to express the vectors u1 and u2 as linear combinations of v1 and v2 in more ways than one. c) Also explain the relevance (regarding existence and unambiguity) of the answers in (a) and (b) for the question of solubility to the equations Ax = ul and Ax = u2 if A is the matrix with columns given by v1 and v2.
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