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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. -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

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
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 16EQ
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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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