3. In R³, consider v₁ = (1,0, -1), V₂ = (1, 0,2), V3 = (0, 1, 1), №₁ = (1, −1, 1). (a) Show that any vector (x, y, z) = R³ can be expressed as a linear combi- nation of the vectors V₁, V2, V3. (b) Find another triplet of the vectors such that the same is no longer achiev- able
3. In R³, consider v₁ = (1,0, -1), V₂ = (1, 0,2), V3 = (0, 1, 1), №₁ = (1, −1, 1). (a) Show that any vector (x, y, z) = R³ can be expressed as a linear combi- nation of the vectors V₁, V2, V3. (b) Find another triplet of the vectors such that the same is no longer achiev- able
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:3. In R³, consider V₁ = (1, 0, −1), V₂ = (1,0, 2), V3 = (0,1,1), V₁ = (1, −1, 1).
(a) Show that any vector (x, y, z) = R³ can be expressed as a linear combi-
nation of the vectors U₁, V2, V3.
(b) Find another triplet of the vectors such that the same is no longer achiev-
able.
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