Interactive Study › Linear Algebra
MAT 102 · DSE · Intake 2/1 · Dr. Ronobir Chandra Sarker
Work through the topics in order. Each one has a short step-by-step lesson and a set of numbered questions you can practise until they are mastered — new numbers every time, full worked solutions, and your progress is recorded when you sign in with your BUBT account.
Dot products, lengths, cosine similarity, the Cauchy–Schwarz inequality and unit vectors — in the setting of a movie-recommendation system. Book §1.1–1.2.
Start ›Read a matrix by its columns: multiplying \(A\mathbf{x}\) and \(AB\), independence, rank, describing \(\mathbf{C}(A)\) as a point / line / plane / all of 3-D, and the factorization \(A = CR\). Book §1.3–1.4.
Start ›Turn \(A\) into a triangle by row operations you perform yourself — typing the multipliers and new rows inside the matrix — then back-substitute. Four system sizes, pivots, row exchanges, and how many solutions a system can have. Book §2.1.
Start ›Pivot and free variables, special solutions, and the complete solution \(\mathbf{x}_p + \mathbf{x}_n\). Book §3.2–3.3. Coming soon.
Gauss–Jordan for \(A^{-1}\), and determinants by cofactors and by pivots. Book §2.2, §5.1–5.2. Coming soon.