Sources, coverage and document notes
What was read, how each document was used, how many questions come from each chapter, and the errors we found in the course materials.
Documents read
| Document | Pages | How it is used |
|---|---|---|
| Lectures/Lecture 1.pdf | 18 | Lecture slides: chapter outline, concept checks |
| Lectures/Lecture 2.pdf | 18 | Lecture slides: chapter outline, concept checks |
| Lectures/Lecture3.pdf | 34 | Lecture slides: chapter outline, concept checks |
| Lectures/Lecture4.pdf | 51 | Lecture slides: chapter outline, concept checks |
| Lectures/Lecture5.pdf | 39 | Lecture slides: chapter outline, concept checks |
| Lectures/Lecture6.pdf | 39 | Lecture slides: chapter outline, concept checks |
| Lectures/Lecture7 .pdf | 28 | Lecture slides: chapter outline, concept checks |
| Sample Tests/Final 2022-2025.pdf | 6 | Past final exam: problems solved in full on the Written page |
| Sample Tests/FinalLA_USTH2019-2020.pdf | 1 | Past final exam: problems solved in full on the Written page |
| Sample Tests/FinalLA_USTH2023-2024_Shift1.pdf | 1 | Past final exam: problems solved in full on the Written page |
| Sample Tests/usthfinal20182019.pdf | 3 | Past final exam: problems solved in full on the Written page |
| Sample Tests/usthfinal20222023.pdf | 2 | Past final exam: problems solved in full on the Written page |
| Sharing Sessions/[BLOCK 2] Sharing Session Linear Algebra.pdf | 30 | Sharing-session slides (scanned, OCR read) |
| Textbooks/Elementary Linear Algebra - 8th Edition.pdf | 471 | Reference reading (chapter map below) |
| Textbooks/Introduction to Linear Algebra - 4th Edition.pdf | 586 | Reference reading (chapter map below) |
| Tutor/A4, B5, B6 - LA - BI15/Exercise Sheet 1 - Systems of Linear Equations.pdf | 2 | Exercise source: every auto-checkable problem is a question; the rest is kept for the written practice |
| Tutor/A4, B5, B6 - LA - BI15/Exercise Sheet 2 - Operations with Matrices.pdf | 3 | Exercise source: every auto-checkable problem is a question; the rest is kept for the written practice |
| Tutor/A4, B5, B6 - LA - BI15/Exercise Sheet 3 - Determinants.pdf | 1 | Exercise source: every auto-checkable problem is a question; the rest is kept for the written practice |
| Tutor/A4, B5, B6 - LA - BI15/Exercise Sheet 4 - Vector Spaces.pdf | 3 | Exercise source: every auto-checkable problem is a question; the rest is kept for the written practice |
| Tutor/A4, B5, B6 - LA - BI15/Exercise Sheet 5 - Inner Product Spaces.pdf | 2 | Exercise source: every auto-checkable problem is a question; the rest is kept for the written practice |
| Tutor/A4, B5, B6 - LA - BI15/Exercise Sheet 6 - Linear Transformations.pdf | 3 | Exercise source: every auto-checkable problem is a question; the rest is kept for the written practice |
| Tutor/A4, B5, B6 - LA - BI15/Exercise Sheet 7 - Eigenvalues and Eigenvectors.pdf | 1 | Exercise source: every auto-checkable problem is a question; the rest is kept for the written practice |
| [LS Gen 5] Final Tutorial/Final Exam Linear Algebra Tutorial - Part 1.pdf | 38 | Final-exam tutoring slides (scanned, OCR read): theory recap and exam-style problems, covered by the bank and the Written papers |
| [LS Gen 5] Final Tutorial/Final Exam Linear Algebra Tutorial - Part 2.pdf | 57 | Final-exam tutoring slides (scanned, OCR read): theory recap and exam-style problems, covered by the bank and the Written papers |
| [LS Gen 5] Final Tutorial/Linear Algebra Summary (UPDATED Gen 16 edition).pdf | 38 | Theory summary with worked exercises: its exercises became questions labelled 'Linear Algebra Summary (Gen 16)'; the slips found in it are listed below |
| [LS Gen 5] Final Tutorial/Tutor Final LA Part 1 - Block 2.pdf | 52 | Final-exam tutoring slides (scanned, OCR read): theory recap and exam-style problems, covered by the bank and the Written papers |
| [LS Gen 5] Final Tutorial/Tutor Final LA Part 2 - Block 2.pdf | 33 | Final-exam tutoring slides (scanned, OCR read): theory recap and exam-style problems, covered by the bank and the Written papers |
PDFs with a text layer were converted with pdftotext; scanned PDFs were OCR'd with tesseract and the formulas were checked against the page images. Where a problem statement mixed text and a figure, only the text-complete parts became questions.
Question coverage per chapter
| Chapter | Total | From course documents | Generated (same style) | Concept checks | Textbook sections |
|---|---|---|---|---|---|
| Ch. 1 Systems of linear equations | 73 | 51 | 14 | 8 | Elementary Linear Algebra (8th ed.) ch. 1 §1.1–1.3 · Strang ch. 2 §2.1–2.3 and §3.3–3.4 |
| Ch. 2 Matrices | 58 | 46 | 9 | 3 | Elementary Linear Algebra ch. 2 §2.1–2.4 · Strang §2.4–2.7 |
| Ch. 3 Determinants | 41 | 28 | 8 | 5 | Elementary Linear Algebra ch. 3 §3.1–3.4 · Strang ch. 5 §5.1–5.3 |
| Ch. 4 Vector spaces | 71 | 54 | 13 | 4 | Elementary Linear Algebra ch. 4 §4.1–4.7 · Strang ch. 3 §3.1–3.6 |
| Ch. 5 Inner product spaces | 43 | 36 | 3 | 4 | Elementary Linear Algebra ch. 5 §5.1–5.4 · Strang ch. 4 §4.1–4.4 |
| Ch. 6 Linear transformations | 77 | 70 | 3 | 4 | Elementary Linear Algebra ch. 6 §6.1–6.4 · Strang ch. 7 §7.1–7.3 |
| Ch. 7 Eigenvalues and eigenvectors | 76 | 67 | 5 | 4 | Elementary Linear Algebra ch. 7 §7.1–7.3 · Strang ch. 6 §6.1–6.4 |
Errors and oddities found in the course documents
Each item below was found by checking our computed answer against the printed one (or when an exercise turned out to be impossible as printed). The quiz uses the computed result.
- Exercise Sheet 3, Ex. 8: The third equation is printed as $5x+4y+2x=4$; read as $5x+4y+2z=4$ (typo).
- Exercise Sheet 3, Ex. 11: As printed, the matrix $\begin{bmatrix}0 & 1 & 1 \\ 1 & 2 & 3 \\ -1 & -1 & -2\end{bmatrix}$ has $\det A=0$, so the inverse requested in the exercise does not exist (probably a typo in the sheet). We keep the exercise as a singular-matrix question: $A\,\operatorname{adj}A=(\det A)I=0$.
- Exercise Sheet 5, Ex. 16: As printed, $x=(-1,4,2)$ is not in the span of $B=\{(0,2,-2),(1,0,-2)\}$ (the third coordinate would have to be $-2$). We use $x=(-1,4,-2)$, which is in the subspace as the exercise intends.
- Linear Algebra Summary (Gen 16), II.2: The notes say that for $AC=BC$ with $C\neq0$ and $C$ not invertible, 'then $A\neq B$'. That is too strong: when $C$ is singular, $A=B$ is simply not guaranteed (it may or may not hold).
- Linear Algebra Summary (Gen 16), III exercise 2: The factorisation is printed as $A(2022A^3+A^2-A)=-3I$; it should be $A(2022A^2+A-I)=-3I$. Also $\det(-3I)=(-3)^n$ for an $n\times n$ matrix, not $-3$. The conclusion (A invertible) is unaffected.
- Linear Algebra Summary (Gen 16), IV.5: The notes say 'S1 ⊆ S2: if S2 is linearly independent then S2 is linearly independent'. The second implication should read: if S2 is linearly independent then S1 (the subset) is linearly independent.
How answers were verified
- All answers are produced by code (sympy exact arithmetic, never typed by hand) and, for source problems, compared with the printed answer key; the build stops if they disagree.
- Distractors are realistic mistakes (sign errors, missing chain-rule factor, transposed matrices, wrong-order composition…), and every distractor is checked to be different from the correct answer.
- Option positions are shuffled with a fixed seed and balanced (A/B/C/D each 25%); the correct option is not systematically the longest.