) Let V = R²X2 be the vector space of 2 x 2 matrices and let L: V → V be defined by L(X) The image of a spanning set is a spanning set for the image. 0 (139) -3 -1 b. Find a basis for ker(L): a. Find L( = c. Find a basis for ran(L): } = 4 [32]×. 8 X. Hint:

) Let V = R²X2 be the vector space of 2 x 2 matrices and let L: V → V be defined by L(X) The image of a spanning set is a spanning set for the image. 0 (139) -3 -1 b. Find a basis for ker(L): a. Find L( = c. Find a basis for ran(L): } = 4 [32]×. 8 X. Hint:

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Determinants

Section3.3: Properties Of Determinants

Problem 63E: Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.

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Question

Let V = R²X2 be the vector space of 2 × 2 matrices and let L : V → V be defined by L(X) = [3
=
The image of a spanning set is a spanning set for the image.
36 3
0
4 [13] ²
=
-3 -1
b. Find a basis for ker(L):
a. Find L
c. Find a basis for ran(L):
}
-4
X. Hint:

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