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Suppose the vectors u, v, x, y, z are distinct vectors in R4, and that the vectors x, y, z are linearly independent. Which of the following are TRUE? (select all that apply) 0 The vectors x+y+z, x-y+z, x + z are linearly independent. The equation ax +by+cz = 0 has only the solution a = b = c = 0. The vectors x + y, y + z, x + z are linearly independent. One of the vectors in the set {x, y, z) can be expressed as a linear combination of the other two. Every vector in R4 can be expressed as a linear combination of the vectors x, y, z. The vectors u, v, x, y, z are linearly independent.

Suppose the vectors u, v, x, y, z are distinct vectors in R4, and that the vectors x, y, z are linearly independent. Which of the following are TRUE? (select all that apply) 0 The vectors x+y+z, x-y+z, x + z are linearly independent. The equation ax +by+cz = 0 has only the solution a = b = c = 0. The vectors x + y, y + z, x + z are linearly independent. One of the vectors in the set {x, y, z) can be expressed as a linear combination of the other two. Every vector in R4 can be expressed as a linear combination of the vectors x, y, z. The vectors u, v, x, y, z are linearly independent.

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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Suppose the vectors u, v, x, y, z are distinct vectors in Rª, and that the vectors x, y, z are linearly independent. Which of the following are TRUE? (select all that apply) 0 The vectors x+y+z, x-y+z, x + z are linearly independent. The equation ax +by+cz = 0 has only the solution a = b = c = 0. The vectors x + y, y+z, x+z are linearly independent. One of the vectors in the set {x, y, z) can be expressed as a linear combination of the other two. Every vector in R4 can be expressed as a linear combination of the vectors x, y, z. The vectors u, v, x, y, z are linearly independent.
Transcribed Image Text:Suppose the vectors u, v, x, y, z are distinct vectors in Rª, and that the vectors x, y, z are linearly independent. Which of the following are TRUE? (select all that apply) 0 The vectors x+y+z, x-y+z, x + z are linearly independent. The equation ax +by+cz = 0 has only the solution a = b = c = 0. The vectors x + y, y+z, x+z are linearly independent. One of the vectors in the set {x, y, z) can be expressed as a linear combination of the other two. Every vector in R4 can be expressed as a linear combination of the vectors x, y, z. The vectors u, v, x, y, z are linearly independent.
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