7. In the vector space L(R²), let T be the transformation defined by b a ( o d) = (c-²3 36) с T b d - 3b a. Is T linear? b. Does there exist a 2x2 matrix A such that AB = T(B) for all 2x2 matrices B? c. Does there exist a 2x2 matrix A such that BA= T(B) for all 2x2 matrices B?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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7. In the vector space L(R²), let T be the transformation defined by
a
T ( c à ) = ( c ²3
с
- 3a
b
d – 3b
a. Is T linear?
b. Does there exist a 2x2 matrix A such that AB = T(B) for all 2x2 matrices B?
c. Does there exist a 2x2 matrix A such that BA = T(B) for all 2x2 matrices B?
Transcribed Image Text:7. In the vector space L(R²), let T be the transformation defined by a T ( c à ) = ( c ²3 с - 3a b d – 3b a. Is T linear? b. Does there exist a 2x2 matrix A such that AB = T(B) for all 2x2 matrices B? c. Does there exist a 2x2 matrix A such that BA = T(B) for all 2x2 matrices B?
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