Proposition 1: Let T: V-> W be a linear transformation of linear spaces V and W, suppose that a set of vectors }} CV has the property that Tví TV3 )} :{T (₁²), T (₂²), T 12,03 } . CV is linearly independent. {0₁ →→ V1, V2, V3 independent. Then, the set of vectors →→ V1, V2, V3 Below is a "proof" of the above proposition. You may use it as a template and upload your proof below. →> → →>> Proof: Suppose that a₁v₁ + a2v₂ + a3v3 = Ō. Then, applying T to both sides we get Since T is a linear transformation, we get Since {T(v²), T (√₂²),T (v₂)} CW is linearly are linear independent we get that
Proposition 1: Let T: V-> W be a linear transformation of linear spaces V and W, suppose that a set of vectors }} CV has the property that Tví TV3 )} :{T (₁²), T (₂²), T 12,03 } . CV is linearly independent. {0₁ →→ V1, V2, V3 independent. Then, the set of vectors →→ V1, V2, V3 Below is a "proof" of the above proposition. You may use it as a template and upload your proof below. →> → →>> Proof: Suppose that a₁v₁ + a2v₂ + a3v3 = Ō. Then, applying T to both sides we get Since T is a linear transformation, we get Since {T(v²), T (√₂²),T (v₂)} CW is linearly are linear independent we get that
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Proposition 1: Let T: V-> W be a linear transformation of linear spaces V and W, suppose that a set
CW is linearly
of vectors
{v}
→→
V1, V2, V3
}}
CV has the property that T
{T (v₁),T (√₂²),T (√₂)}
(v
independent. Then, the set of vectors
{0₁, 02, 07 }
Below is a "proof" of the above proposition. You may use it as a template and upload your proof below.
→
→
→
Proof: Suppose that a₁v₁ + a2v₂ + a3v3
Then, applying T to both sides we get
Since T is a linear transformation, we get
T
Since {7 (5),(6). (6)
{T
T
T
=
V3 CV is linearly independent.
Ō.
are linear independent we get that
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
