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Consider the following vectors in R³. a = (1, 0,4)7, g = (1,2,3)^, g = (2,2,7)^, A = (0, −2, 1)^, s = (0, 0, 1)7. (a) Given that R³ = span(₁, 2, 3, 4, 5), 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. a = (1, 0,4)7, g = (1,2,3)^, g = (2,2,7)^, A = (0, −2, 1)^, s = (0, 0, 1)7. (a) Given that R³ = span(₁, 2, 3, 4, 5), 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
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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Consider the following vectors in R³. ₁ = (1, 0,4), ₂ = (1,2,3), z =(2, 2, 7), ₁ = (0, -2, 1), u = (0, 0, 1). (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).
Transcribed Image Text:Consider the following vectors in R³. ₁ = (1, 0,4), ₂ = (1,2,3), z =(2, 2, 7), ₁ = (0, -2, 1), u = (0, 0, 1). (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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