Explain why S is not a basis for R³.S = {(8, 6, 13), (6, 1, 4), (3, 1,-5), (0, 8, 3)}OS is linearly dependent.OS does not span R³.OS is linearly dependent and does not span R³.J

Definition of a basis of ℝ3 : A set S is said to be a basis of ℝ3 if i) It is linearly independent…

Answered: Explain why S is not a basis for R³. S…

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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Show that the set {(1, 2, 1), (2, 1, 0), (1, -1, 2) forms a basis for V3 (R).
1. Determine whether the vectors (1,-1) and (1, 1)T are linearly inde- pendent or not. 2. Show that the vectors (1,0,0), (1, 1, 0) and (1,1,1) form a basis of R³. 3. Suppose that the vectors (1, 2, -1,0) and (1,3,2,0) span the sub- space U of R4. Determine whether the vector (1, 1, 1, 0) belongs to U or not.
Explain why S is not a basis for R2. S = {(2, 5), (6, 15)} O sis linearly dependent. O S does not span R2. O is linearly dependent and does not span R2.
2
Explain why S is not a basis for R². S = {(3, 7), (1, 0), (0, 1)} OS is linearly dependent. O S does not span R². O S is linearly dependent and does not span R².
1. Vectors v1 = (1,1,1,1,0), v2 = (-1,1,0,0,0), v3 = (1,1,-1,-1,0), v4 = (0,0,2,-2,0) and v5 = (0,0,0,0,2) form an orthogonal basis for a of R5 and X = (-3, -2,5,1,-4). Find the coordinates of X with respect to the given basis.
Exercise 4.3 Find all the vectors of R³ which have the same coordinates in the canonical basis and in the basis = {(5, 18, 22), (-1,-8,-1), (1,-1, 12)}.

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Explain why S is not a basis for R³. S = {(8, 6, 13), (6, 1, 4), (3, 1, -5), (0, 8, 3)) OS is linearly dependent. OS does not span R³. OS is linearly dependent and does not span R³.