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(a) ( satisfies Find all possible bases B for R² such that the linear transformation or show that no such basis exists. 4: R² R² * (² ²) v VI 56 [49]8 = (²₂8) 7

(a) ( satisfies Find all possible bases B for R² such that the linear transformation or show that no such basis exists. 4: R² R² * (² ²) v VI 56 [49]8 = (²₂8) 7

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 8EQ
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(a) ( satisfies or show that no such basis exists. (b) Find all possible bases B for R² such that the linear transformation and that 4: R² R² VI * (²²) ▼ 56 [49]8 = (²₂8) 7 Suppose that 0: M23 (R) → P is a linear transformation such that 0(E)=0 for all i ≤ j 0(A) = z²+z for some A € M₂3 (R). Does there exist a matrix B € M₂,3 (R) such that (B) = z-1? Justify your answer.
Transcribed Image Text:(a) ( satisfies or show that no such basis exists. (b) Find all possible bases B for R² such that the linear transformation and that 4: R² R² VI * (²²) ▼ 56 [49]8 = (²₂8) 7 Suppose that 0: M23 (R) → P is a linear transformation such that 0(E)=0 for all i ≤ j 0(A) = z²+z for some A € M₂3 (R). Does there exist a matrix B € M₂,3 (R) such that (B) = z-1? Justify your answer.
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