Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Show that every vector in T1 = span {(1,0,0); (0,1,0); (0,0,1)} are in also in T2 Та %3 span {(1,1,0); (0,0,1); (1,0,1)}, i.e. show explicitly how , in T2 corresponds to some given t, in T1.

Show that every vector in T1 = span {(1,0,0); (0,1,0); (0,0,1)} are in also in T2 Та %3 span {(1,1,0); (0,0,1); (1,0,1)}, i.e. show explicitly how , in T2 corresponds to some given t, in T1.

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 show work 

6. Show that every vector in \( T_1 = \text{span} \{ (1,0,0); (0,1,0); (0,0,1) \} \) are also in \[ T_2 = \text{span} \{ (1,1,0); (0,0,1); (1,0,1) \}, \] i.e., show explicitly how \( \vec{t}_2 \) in \( T_2 \) corresponds to some given \( \vec{t}_1 \) in \( T_1 \).
Transcribed Image Text:6. Show that every vector in \( T_1 = \text{span} \{ (1,0,0); (0,1,0); (0,0,1) \} \) are also in \[ T_2 = \text{span} \{ (1,1,0); (0,0,1); (1,0,1) \}, \] i.e., show explicitly how \( \vec{t}_2 \) in \( T_2 \) corresponds to some given \( \vec{t}_1 \) in \( T_1 \).
Expert Solution
Step 1

Consider the vector space T1=span1,0,0,0,1,0,0,0,1 and T2=span1,1,0,0,0,1,1,0,1

Let t1→=a,b,c∈T1 be an arbitrary vector. Therefore it can be represented as:

                     t1→=a,b,c=a1,0,0+b0,1,0+c0,0,1

Let l,m,n∈T2 be an arbitrary vector. Therefore it can be represented as:

             l,m,n=d1,1,0+e0,0,1+f1,0,1l,m,n=d+f,d,e+f

Solving them for d,e,f, we have:

                       l=d+fm=dn=e+f

Therefore d=m, f=l-m and e=m+n-l

steps

Step by step

Solved in 2 steps

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