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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).

Advanced Engineering Mathematics
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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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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