Consider the following vectors in R³. 1 = (1,0,4)^, 2 = (1,2,3)^, ūs = (2,2, 7)^, đa = (0, –2, 1)^, is = (0, 0, 1). (a) Given that R³ = span(ū₁, 2, 3, 4, ū5), reduce these vectors to a linearly independent set and hence form a basis for R³. (b) Write (x, y, z)¹ € R³ as a linear combination of the three vectors you obtained in (a).
Consider the following vectors in R³. 1 = (1,0,4)^, 2 = (1,2,3)^, ūs = (2,2, 7)^, đa = (0, –2, 1)^, is = (0, 0, 1). (a) Given that R³ = span(ū₁, 2, 3, 4, ū5), reduce these vectors to a linearly independent set and hence form a basis for R³. (b) Write (x, y, z)¹ € R³ as a linear combination of the three vectors you obtained in (a).
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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Transcribed Image Text:4. Consider the following vectors in R³.
ũ₁ = (1,0, 4)¹, ū₂ = (1, 2, 3)¹, ū3 = (2,2, 7), ū₁ = (0, 2, 1)¹, ū5 = (0, 0, 1)¹.
A s
(a) Given that R³ = span(ū1, ū2, Ū3, ū4, ū5), reduce these vectors to a linearly
independent set and hence form a basis for R³.
(b) Write (x, y, z)¹ € R³ as a linear combination of the three vectors you
obtained in (a).
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