Let V = R2X2 be the vector space of 2 x 2 matrices and let L: V → V be defined by L(X) Hint: The image of a spanning set is a spanning set for the image. -5 4 [ { } }) 2 b. Find a basis for ker(L): a. Find L( c. Find a basis for ran(L): 86 = 7¹]x. X. 5 -20 4

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 63EQ
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Let V = R²x2 be the vector space of 2 x 2 matrices and let L: V → V be defined by L(X) =
Hint: The image of a spanning set is a spanning set for the image.
a. Find L(
{
-5
2
{
-5
b. Find a basis for ker(L):
=
c. Find a basis for ran(L):
"
}
}
5
-20
-1
4
X.
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) = Hint: The image of a spanning set is a spanning set for the image. a. Find L( { -5 2 { -5 b. Find a basis for ker(L): = c. Find a basis for ran(L): " } } 5 -20 -1 4 X.
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