Suppose ....,V4}is a linearly dependent spanning set for a vector space V. Show that each w in V can be expressed in more than one way as a linear combination of V4. [Hint: Let w = k¡v1 + •…+ k4v4 /1, . . . , V4 V1, ..., be an arbitrary vector in V. Use the linear dependence of {V1,..., V4 to produce another representation of w , V4.] as a linear combination of V1,,...
Suppose ....,V4}is a linearly dependent spanning set for a vector space V. Show that each w in V can be expressed in more than one way as a linear combination of V4. [Hint: Let w = k¡v1 + •…+ k4v4 /1, . . . , V4 V1, ..., be an arbitrary vector in V. Use the linear dependence of {V1,..., V4 to produce another representation of w , V4.] as a linear combination of V1,,...
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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