L: V → V be defined by L(X) Let V = R2X2 be the vector space of 2 x 2 matrices and let R²×2 -12 -4 X. Hint: The image of a 1 3 spanning set is a spanning set for the image. 118 1 422) b. Find a basis for ker(L): a. Find L( { c. Find a basis for ran(L): 1 [ { } }

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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L: V→ V be defined by L(X)
Let V = R2X2 be the vector space of 2 x 2 matrices and let
R²×2
-12
-4
X. Hint: The image of a
1
3
spanning set is a spanning set for the image.
18
4(12)
b. Find a basis for ker(L):
a. Find L(
{
c. Find a basis for ran(L):
1 [
{
}
}
Transcribed Image Text:L: V→ V be defined by L(X) Let V = R2X2 be the vector space of 2 x 2 matrices and let R²×2 -12 -4 X. Hint: The image of a 1 3 spanning set is a spanning set for the image. 18 4(12) b. Find a basis for ker(L): a. Find L( { c. Find a basis for ran(L): 1 [ { } }
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