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Let V = R²×2 be the vector space of 2 x 2 matrices and let L: V → V -12 - 4 2] 6 be defined by L(X) = spanning set for the image. -4 -2 a. Find L( b. Find a basis for ker(L): - 18 c. Find a basis for ran(L): 18 318 X. Hint: The image of a spanning set is a } }

Let V = R²×2 be the vector space of 2 x 2 matrices and let L: V → V -12 - 4 2] 6 be defined by L(X) = spanning set for the image. -4 -2 a. Find L( b. Find a basis for ker(L): - 18 c. Find a basis for ran(L): 18 318 X. Hint: The image of a spanning set is a } }

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let V = R²×2 be the vector space of 2 × 2 matrices and let L : V → V -12 X. Hint: The image of a spanning set is a 6 be defined by L(X) = spanning set for the image. a. Find L( { -1 -4 -2 -2 - = b. Find a basis for ker(L): 18 c. Find a basis for ran(L): 188188 }
Transcribed Image Text:Let V = R²×2 be the vector space of 2 × 2 matrices and let L : V → V -12 X. Hint: The image of a spanning set is a 6 be defined by L(X) = spanning set for the image. a. Find L( { -1 -4 -2 -2 - = b. Find a basis for ker(L): 18 c. Find a basis for ran(L): 188188 }
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