Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(d) Determine whether the set W = {(x₁,x₂,4):x, and x, are real numbers is a subspace with the standard operations. Justify your answer. fe) Determine whether the rat 12

(d) Determine whether the set W = {(x₁,x₂,4):x, and x, are real numbers is a subspace with the standard operations. Justify your answer. fe) Determine whether the rat 12

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
See similar textbooks
icon
Related questions
Question

please can you redo the question answer by using guass jordan elimation with proper working . question part e

(a) Given u =(3,-1,2,3) and v= (0,2,2,1) in R¹. Find 3u-2v. =(4,4,5) as a linear combination of u, = (1,2,3), u, = (-2,0,1) and u, = (1,0,0). (b) Write v=(4,4,5) (c) Determine whether the set R², with the operations (x₁, y₁) + (x₂, y₂ ) = (x,,0) and c(x, y) = (x,cy) is a vector space. If it is, verify each vector space axiom. If not, state all vector space axioms that fail. (d) Determine whether the set W = {(x₁,x₂,4): x, and x₂ are real numbers is a subspace of R³ with the standard operations. Justify your answer. (e) Determine whether the set S = {x²-2x,x² +8,x¹-x²₁x² -4} spans P₁.
Transcribed Image Text:(a) Given u =(3,-1,2,3) and v= (0,2,2,1) in R¹. Find 3u-2v. =(4,4,5) as a linear combination of u, = (1,2,3), u, = (-2,0,1) and u, = (1,0,0). (b) Write v=(4,4,5) (c) Determine whether the set R², with the operations (x₁, y₁) + (x₂, y₂ ) = (x,,0) and c(x, y) = (x,cy) is a vector space. If it is, verify each vector space axiom. If not, state all vector space axioms that fail. (d) Determine whether the set W = {(x₁,x₂,4): x, and x₂ are real numbers is a subspace of R³ with the standard operations. Justify your answer. (e) Determine whether the set S = {x²-2x,x² +8,x¹-x²₁x² -4} spans P₁.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS