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.
Vectors and linear combinations (\(A\mathbf{x}\) as a combination of columns), lengths and angles from dot products (unit vectors, perpendicularity, cosine similarity, Schwarz and triangle inequalities), matrices and their column spaces, and multiplication \(AB\) with \(A = CR\). Book §1.1–1.4.
Start ›Gaussian elimination and Gauss–Jordan in one place. Build the whole reduction yourself — circled pivots, your multipliers, your rows, row swaps for zero rows — on any size from 2×2 to 4×4, down to the echelon form and on to the RREF. Then exam-style write-ups: solving systems (one / no / infinitely many solutions, with the picture), reading RREFs, \(A^{-1}\) from \([\,A\,|\,I\,]\), and transposes & symmetric matrices. Book §2.1–2.4, §3.2.
Start ›Factor any matrix as \(A = CR\) with Gauss–Jordan elimination — build the whole reduction to \(R_0=\mathrm{rref}(A)\) yourself, then read off \(C\) (pivot columns of \(A\)) and \(R\). Subspaces, column and row spaces and when \(A\mathbf{x}=\mathbf{b}\) is solvable, the nullspace and its special solutions, the complete solution \(\mathbf{x}_p+\mathbf{x}_n\), independence and bases, all four subspaces with their dimensions \(r,\,r,\,n-r,\,m-r\) — plus a live picture where you drag \(\mathbf{x}\) and watch \(A\mathbf{x}\) move through the subspaces. Book §3.1–3.5.
Start ›By cofactors and by pivots. Book §5.1–5.2. Coming soon.