8. Ax = b FINALLY Explained! 🔥 Particular Solution, General Solution, Rank & Null Space

Confused by A x = b , rank, free variables, particular solutions, and general solutions? You’re not alone. 😭 In this video, we break down one of the most important concepts in Linear Algebra from the ground up — without skipping the logic. By the end, you’ll know exactly how to: ✅ Solve a system of the form Ax=b ✅ Determine whether a solution exists ✅ Find the rank of a matrix ✅ Use rank(A) vs rank([A|b]) to identify the number of solutions ✅ Understand pivot variables vs free variables ✅ Find a particular solution ✅ Find the homogeneous solution Ax=0 ✅ Find the general solution ✅ Find a basis for the null space ✅ Understand the Rank–Nullity Theorem ✅ Know when a system has 0, 1, or infinitely many solutions