(d) Suppose the three vectors x, y, z E R³ are known to be linearly independent. Are the three vectors u = x – y, v = x – z, and w = y – z also linearly independent? Explain.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let A be the matrix:
0 a² – 2
a
|
A =
1
1
-1
а — 1
a
Transcribed Image Text:Let A be the matrix: 0 a² – 2 a | A = 1 1 -1 а — 1 a
(d) Suppose the three vectors x, y, z E R³ are known to be linearly independent. Are
the three vectors u = x – y, v = x – z, and w = y – z also linearly independent?
Explain.
Transcribed Image Text:(d) Suppose the three vectors x, y, z E R³ are known to be linearly independent. Are the three vectors u = x – y, v = x – z, and w = y – z also linearly independent? Explain.
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