Let V = R²x2 be the vector space of 2 x 2 matrices and let L: V → V be defined by L(X) = ()- = b. Find a basis for ker(L): a. Find L( c. Find a basis for ran(L): 12 -16 -3 X. Hint: The image of a spanning set is a spanning set for the image. 4

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section: Chapter Questions
Problem 10RQ
icon
Related questions
Question
Let V = R²x2 be the vector space of 2 x 2 matrices and let L: V → V be defined by L(X) =
()-
=
b. Find a basis for ker(L):
a. Find L(
c. Find a basis for ran(L):
12
-16
-3
X. Hint: The image of a spanning set is a spanning set for the image.
4
Transcribed Image Text:Let V = R²x2 be the vector space of 2 x 2 matrices and let L: V → V be defined by L(X) = ()- = b. Find a basis for ker(L): a. Find L( c. Find a basis for ran(L): 12 -16 -3 X. Hint: The image of a spanning set is a spanning set for the image. 4
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage