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
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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e280540-f1eb-4df2-8a7a-9764285a2889%2F9755ff8a-cce6-4344-8065-74e7369f091c%2F9xc633o_processed.jpeg&w=3840&q=75)
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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