Algebra 2 Tutorial: Vector Spaces and Linear Maps

This document is a **first-year undergraduate mathematics tutorial** from the **University of Tipaza’s Faculty of Science**, dated February 2026. The primary focus of the coursework is **Algebra 2**, specifically covering the fundamental properties of **vector spaces and linear maps**. Students are tasked with identifying **subspaces**, calculating **bases**, and determining the **dimensions** of various mathematical sets. Additionally, the exercises require learners to analyze **linear transformations** to determine their **kernels, images, and ranks**. The final sections challenge students to evaluate the **bijectivity** of functions and calculate the **inverse** of specific isomorphisms.