Example 2. Consider the group R² of vectors for r, y real. This is a group under com- () - () -G) b' we have (x+u` ponentwise addition: u + a Given a 2 x 2 matrix M= \y+ v/ a group homomorphism Lm:R² →R² defined by ах + by' cк+ dy a LM = The kernel of Lm is called the nullspace of the matrix M (or the linear function LM) in linear algebra. See Definition 7.2.3. Exercise 3.5.3 Show that Lm in example 2 is indeed a group homomorphism. What is its kernel?

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