and the transformation S: M → R²Let M be the vector space of symmetric 2x2 matrices, the vector space R2defined bys( ) = (a + c,b)%3Da) Find the kernel of S, a base and its dimension.b) Obtain the range of S, its standard base and its dimension.

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Answered: Let M be the vector space of symmetric…

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 M be the vector space of symmetric 2x2 matrices, the vector space R² and the transformation S: M → R² defined by s(: )= (a + c, b) a) Find the kernel of S, a base and its dimension. b) Obtain the range of S, its standard base and its dimension.