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Question In each case determine if x lies in U = span{y, z}. If x is in U, write it as a linear combination of y and z; if x is not in U, show why not. a) x = (2, -1, 0, 1), y = (1, 0, 0, 1), and z = (0, 1, 0, 1). b) x = (1, 2, 15, 11), y = (2, -1, 0, 2), and z = (1, -1, -3, 1). c) x = (8, 3, -13, 20), y = (2, 1, -3, 5), and z = (-1, 0, 2, -3). d) x = (2, 5, 8, 3), y = (2, -1, 0, 5), and z = (-1, 2, 2, -3).

Question In each case determine if x lies in U = span{y, z}. If x is in U, write it as a linear combination of y and z; if x is not in U, show why not. a) x = (2, -1, 0, 1), y = (1, 0, 0, 1), and z = (0, 1, 0, 1). b) x = (1, 2, 15, 11), y = (2, -1, 0, 2), and z = (1, -1, -3, 1). c) x = (8, 3, -13, 20), y = (2, 1, -3, 5), and z = (-1, 0, 2, -3). d) x = (2, 5, 8, 3), y = (2, -1, 0, 5), and z = (-1, 2, 2, -3).

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 4CM: Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4,...
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Question . In each case determine if x lies in U = span{y, z}. If x is in U, write it as a linear combination of y and z; if x is not in U, show why not. a) x = (2, -1, 0, 1), y = (1, 0, 0, 1), and z = (0, 1, 0, 1). b) x = (1, 2, 15, 11), y = (2, -1, 0, 2), and z = (1, -1, -3, 1). c) x = (8, 3, -13, 20), y = (2, 1, -3, 5), and z = (-1, 0, 2, -3). d) x = (2, 5, 8, 3), y = (2, -1, 0, 5), and z = (-1, 2, 2, -3).
Transcribed Image Text:Question . In each case determine if x lies in U = span{y, z}. If x is in U, write it as a linear combination of y and z; if x is not in U, show why not. a) x = (2, -1, 0, 1), y = (1, 0, 0, 1), and z = (0, 1, 0, 1). b) x = (1, 2, 15, 11), y = (2, -1, 0, 2), and z = (1, -1, -3, 1). c) x = (8, 3, -13, 20), y = (2, 1, -3, 5), and z = (-1, 0, 2, -3). d) x = (2, 5, 8, 3), y = (2, -1, 0, 5), and z = (-1, 2, 2, -3).
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