(Solved): Determine the following linear maps of vector spaces over R are isomorphism or not. If it is an is ...

Determine the following linear maps of vector spaces over R are isomorphism or not. If it is an isomorphism, find its inverse map (Hint: inverse of matrices). If it is not an isomorphism, briefly explain why. (1) (Rotation by 60°) L: R² R² such that ?3 (x, y) ? (2 By, ³x + y). (2) (Reflection about x-axis) L: R2. ? R2 such that (x, y) ? (x, y). (3) L: R³ ? R³ such that (x, y, z) ? (x + 2y + 3z, 4x + 5y + 6z, 7x + 8y +9z).