Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
7. What basis for V = M(n, R) does Theorem 3.3 i) yield when applied to T(A) = A + AT, with W M(n, R), when using the standard basis {eje + eje}

7. What basis for V = M(n, R) does Theorem 3.3 i) yield when applied to T(A) = A + AT, with W M(n, R), when using the standard basis {eje + eje}

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
See similar textbooks
icon
Related questions
Question

plz

7. What basis for V = M(n, R) does Theorem 3.3 i) yield when applied to T(A) = A + AT, with W M(n, R), when using the standard basis {eje + ejef}i<i<i<n U{eie?}i=1...n for symmetric matrices (Hint: This too is in the notes). Explain your answer.
Transcribed Image Text:7. What basis for V = M(n, R) does Theorem 3.3 i) yield when applied to T(A) = A + AT, with W M(n, R), when using the standard basis {eje + ejef}i<i<i<n U{eie?}i=1...n for symmetric matrices (Hint: This too is in the notes). Explain your answer.
Th 3.3 i): Let T V W be linear with r = rank (T). Let {w₁,..., w,} be a basis for Rg(T). Let 0; for i = 1,..., r be any choice of elements of V satis- fying T(v₁) = w₁, Vi = 1, ..., r. Let v = nullity (T) and let {₁,..., vy} be a basis for Ker(T). Then {V₁, ..., Ur, U1, ..., U is a basis for V.
Transcribed Image Text:Th 3.3 i): Let T V W be linear with r = rank (T). Let {w₁,..., w,} be a basis for Rg(T). Let 0; for i = 1,..., r be any choice of elements of V satis- fying T(v₁) = w₁, Vi = 1, ..., r. Let v = nullity (T) and let {₁,..., vy} be a basis for Ker(T). Then {V₁, ..., Ur, U1, ..., U is a basis for V.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS