Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
Let P = (0, 1, 0), Q
Recall that a vector of the form
=
w = t₁OP+t₂00
(0, 0, 2), and O = (0, 0, 0).
is called the linear combination of OP and O. What can you say about w
under the following assumptions?
If t₁ + t2 = 1? ¹
If t₁ + t₂ = 1 and t₁ ≥ 0?
If t₁ ≥ 0, t₂ ≥ 0 and t₁ + t2 ≤ 1?
Hint: the line passing through P and Q can be described by
OP + tPQ = OP + t(OQ – OỈ).
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Transcribed Image Text:Let P = (0, 1, 0), Q Recall that a vector of the form = w = t₁OP+t₂00 (0, 0, 2), and O = (0, 0, 0). is called the linear combination of OP and O. What can you say about w under the following assumptions? If t₁ + t2 = 1? ¹ If t₁ + t₂ = 1 and t₁ ≥ 0? If t₁ ≥ 0, t₂ ≥ 0 and t₁ + t2 ≤ 1? Hint: the line passing through P and Q can be described by OP + tPQ = OP + t(OQ – OỈ).
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