Determine whether S is a basis for the indicated vector space.S = {(0, 0, 0), (2, 3, 5), (5, 4, 2)} for R3S is a basis of R3.S is not a basis of R.

The given set is S=(0, 0, 0), (2, 3, 5), (5, 4, 2). We have to determined whether the set S is a…

Answered: Determine whether S is a basis for the…

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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Determine whether S is a basis for the indicated vector space. S = {(2, -1, 0, 0), (0, -1, 0, 2), (0, 3, 4, 0), (5, 0, 0, 0)} for R4 O sis a basis of R4. O Sis not a basis of R4.
Let {1, 2, 3, 4, 5, 6} be the standard basis in R6. Find the length of the vector = 3₁ - 22 - 2ě3 - 2ě4 – 2e5 - 3ē6. #
Determine whether {V₁, V2, V3} is a basis for Ⓡ³. V1 = 4, V2 8 = 0 V3 -4 -16
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.
: Let S = {v1, v2}, where v = standard vectors when added to the set S produces a basis for R? (6,-5, 7,-1) and v2 = (-12, 20, -28, 4). Which of the following combination of (A) v3 = (1, 0, 0, 0), v4 = (0, 0, 1, 0) and vs = (0, 0, 0, 1) (B) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0, 0, 0, 1) (C) v3 = (1, 0, 0, 0) and v4 = (0, 0, 0, 1) (D) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0. 0, 1, 0) (E)v3 = (1, 0, 0, 0) and v4 = (0, 1, 0, 0) (F) v3 = (1, 0, 0, 0) and v4 = (0, 0, 1, 0) (G) v3 = (0, 1, 0, 0) and v4 = (0, 0, 0, 1) %3D %3D (H) v3 = (0, 1, 0, 0), v4 = (0, 0, 1, 0) and vs = (0. 0, 0, 1) %3D
The coordinate vector of the vector (1,2,2) in the basis B = {u= (1,1,1); v = (1,0,1); w= (0,0,1) } is : O A. (1,2,2) O B. (2,-1,1) O C. (2,1,3) O D. (1,2,1)

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Determine whether S is a basis for the indicated vector space. s = {(0, 0, 0), (2, 3, 5), (5, 4, 2)} for R3 O sis a basis of R3. O sis not a basis of R3.