Let B = {(1, 1, 1), (1, 5, -3), (2, 2, 1)}. Show that B is a basis for R'. For the given %3D vector w = (8, -4, -12) find (w)B.
Let B = {(1, 1, 1), (1, 5, -3), (2, 2, 1)}. Show that B is a basis for R'. For the given %3D vector w = (8, -4, -12) find (w)B.
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:Let B =
{(1, 1, 1), (1, 5, -3), (2, 2, 1)}. Show that B is a basis for R'. For the given
vector w = (8, -4, -12) find (w)B.
Expert Solution
Step 1
To solve the following, we use the standered result of basis and spanning set
Basis- Let V is any vactor space
V={v1, v2,.......,vn} is the set of vactors in v them V is called basis, if
(1) V is linearly independent
(2) V span the whole vactor space
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