Part of the expanding PassProfessor catalog: This program is in the works — a chapter-simulation program covering the full scope of a linear algebra course, organized chapter by chapter. Join the notify list and we will email you the day it launches.
This program is part of the expanding PassProfessor catalog — join the notify list and we’ll email you when enrollment opens.
PassProfessor’s Linear Algebra program is a chapter-simulation program for students taking a linear algebra course. You pick the course, then pick the textbook and edition your class uses, and the program builds chapter-based simulation exams optimized for that book’s chapter order — so the practice you do this week matches the chapter your instructor is teaching this week. The program is organized across 14 chapters plus in-depth practice sets, an applied computation set, and an integrative synthesis set, covering systems of linear equations and elimination, matrices and matrix operations, inverses, determinants, vector spaces and subspaces, span, linear independence, basis and dimension, rank, linear transformations, eigenvalues and eigenvectors, diagonalization, and orthogonality with least squares. There is no licensing exam at the end of a linear algebra course — there is your instructor’s exam, chapter by chapter — and this program is built to rehearse exactly that.
PassProfessor’s Linear Algebra program is a chapter-simulation program for the undergraduate linear algebra course: original practice organized chapter by chapter — systems of equations, matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, and orthogonality — matched by textbook and edition so chapter drills and timed simulation exams follow the chapter your instructor is teaching. It rehearses your instructor’s chapter tests and finals — there is no licensing exam for a college course — with results reported by chapter.
What this program is — and what it is not
It is a simulation of your course, not a licensing product. Licensing-exam prep rehearses one fixed, official exam. A college course works differently: your instructor chooses the textbook, sets the chapter order, and writes the exams. This program is designed around that reality. The textbook-and-edition selector aligns the simulations to the chapter sequence of the book your course actually uses, and chapter drills let you practice one chapter at a time, at the point in the semester when you need it.
It is not published, sponsored, or endorsed by any textbook publisher or author. PassProfessor is an independent study provider. The program is never branded or titled under a textbook’s name, and nothing in it reproduces textbook text, textbook figures, or a publisher’s test bank. Selecting your textbook only tells the program which chapter order to organize your practice around.
Every question is original. The bank was built from the published structure of a linear algebra course — the standard chapter sequence and topic scope the discipline itself uses — and every stem, scenario, and answer option was written from scratch and checked against verified disciplinary facts. Sources supplied facts and course structure only; the questions are ours.
What’s included
Practice organized the way your course is organized. The bank follows a 14-chapter structure that mirrors the standard linear algebra course, from systems of linear equations and Gaussian elimination through symmetric matrices and quadratic forms, in outline, plus in-depth practice sets, an applied computation set, and an integrative synthesis set. The full chapter-by-chapter breakdown is in the coverage table below.
Chapter drills. Practice a single chapter — only that chapter — until the misses stop repeating. Finished the eigenvalue lectures? Drill that chapter until finding a characteristic polynomial feels automatic. Determinants test in ten days? Work the determinants chapter in sequence, the way your course presents it.
Chapter-based simulation exams. When a chapter test or a unit exam approaches, sit a timed simulation built from the chapters it covers, in the proportions your selected textbook’s organization suggests. Simulations draw questions you have not seen first, so a second or third run at the same chapter is a fresh test, not a memory exercise.
A textbook-and-edition selector. Different textbooks divide the same material into chapters differently — one book’s single chapter is another book’s two. When you select the textbook and edition your course uses, the program maps its bank onto that book’s chapter organization, so the chapter number in your practice means the same chapter in your syllabus.
Results broken down by chapter and topic. Your practice results report by chapter, so a weak area — say, rank and nullity, or diagonalization — shows up in your data while there is still time to fix it, not for the first time on a graded exam.
A note on editions and course versions. Instructors adopt different textbooks and different editions of the same textbook, and departments periodically revise the course itself. The bank’s organization follows the discipline’s standard chapter structure — the sequence the field itself teaches — and the selector maps that structure onto your edition’s numbering, so a chapter that your book splits in two, or merges into one, still lines up with the practice built for it. Where an instructor reorders chapters, chapter drills can be assembled in your course’s order; the practice follows the syllabus, not the other way around.
The course at a glance
Linear Algebra has no single official exam, so there is no official exam-facts table to publish — your instructor’s syllabus is the authority for your course’s test dates, formats, and grading. What is standard is the scope of the discipline itself, summarized here as course background. For the full picture of what a linear algebra course covers and how to study it, see our Linear Algebra study guide.
| Undergraduate linear algebra — the course this program simulates | |
|---|---|
| Course type | Undergraduate college course (a core mathematics course for mathematics, engineering, computer science, physics, and data-oriented programs; typically taken after introductory calculus, though course prerequisites vary by institution) |
| Standard scope | Systems of linear equations — Gaussian elimination, row echelon forms, and solution structure; matrices and matrix operations, inverses, and elementary matrices; determinants and their properties; vector spaces and subspaces; span, linear independence, basis, dimension, and coordinates; row, column, and null spaces and rank; linear transformations and their matrices; eigenvalues and eigenvectors; diagonalization and its applications; inner products, orthogonality, Gram-Schmidt, orthogonal projection, and least squares; symmetric matrices and quadratic forms in outline |
| How the course is assessed | Instructor-set chapter tests, unit exams, and a final — formats and weights vary by instructor and institution |
| This program’s bank | Chapter-based practice across 14 chapters + in-depth, applied, and synthesis sets |
| Program format | Chapter drills and chapter-based simulation exams, organized by your selected textbook/edition |
How the practice maps to the course
The program follows the standard chapter organization of the course, below. Chapter drills draw only from the chapter you select, and simulation exams can be built over any set of chapters.
| Chapter | Coverage |
|---|---|
| Systems of Linear Equations and Gaussian Elimination | — |
| Matrices and Matrix Operations | — |
| Matrix Inverses and Elementary Matrices | — |
| Determinants and Their Properties | — |
| Vector Spaces and Subspaces | — |
| Span and Linear Independence | — |
| Basis, Dimension, and Coordinates | — |
| Row, Column, and Null Spaces and Rank | — |
| Linear Transformations and Their Matrices | — |
| Eigenvalues and Eigenvectors | — |
| Diagonalization and Its Applications | — |
| Inner Products and Orthogonality | — |
| Gram-Schmidt, Orthogonal Projection, and Least Squares | — |
| Symmetric Matrices and Quadratic Forms in Outline | — |
The closing chapter deserves a note: symmetric matrices and quadratic forms are treated in outline in many first courses and in depth in others, and some courses place orthogonality before eigenvalues rather than after. The program’s textbook selector maps practice onto your book’s organization, so your drills carry the chapters — and the order — your course actually uses.
How to use it
- Join the notify list today. When the program opens, set up your course first: select Linear Algebra, then select the textbook and edition your syllabus names.
- Drill the chapter you are in. After each lecture block, drill that chapter while the material is current. Short, chapter-matched practice beats a single long session the night before the test.
- Watch your chapter breakdown. Your results show which chapters are costing you. Return to the weakest chapter’s drill before moving on — linear algebra builds concept on concept — elimination produces rank, rank explains solution structure, and vector-space language is what eigenvalues and transformations are stated in, so an early gap resurfaces in every later chapter.
- Simulate before each graded test. In the days before a chapter test or unit exam, sit a timed simulation over exactly the chapters it covers. Practice the pacing and the question style, not just the facts.
- Use the integrated set before midterms and finals. The cross-chapter questions combine chapters the way cumulative exams do. They are the closest rehearsal for a final that reaches back to the start of the term.
Frequently asked questions
Is this a licensing exam prep program? No. Linear algebra is a college course, not a licensed credential, and there is no official linear algebra exam at the end of it. This is a chapter-simulation program: it rehearses the tests your own instructor gives, chapter by chapter, using original practice built to the standard scope of the undergraduate course.
Which textbook does the program follow? The program is organized around the standard chapter structure of the linear algebra course, and the textbook-and-edition selector maps practice onto your book’s chapter order when you set up your course. No textbook is named, branded, or reproduced — the selector only aligns chapter numbering.
Do I need calculus before linear algebra? Institutional prerequisites vary — many programs require some calculus first, others admit students directly. The course itself uses little calculus; its real demands are algebraic fluency and comfort with definitions. Your catalog and syllabus state your institution’s rule.
Does the program cover proofs as well as computation? It covers the course the way the course is taught: computation chapters and theory chapters both, including definition checks, equivalent-condition reasoning, and short justification items of the kind undergraduate courses examine. The balance in your own exams is your instructor’s, described in your syllabus.
Can I practice just one chapter? Yes — that is the core of the design. Chapter drills draw only from the chapter you select, and simulation exams can be built over any set of chapters, so your practice can match a single chapter test, a unit exam, or a cumulative final.
My course orders eigenvalues before orthogonality. Will the practice still line up? In most cases, yes. Courses differ mainly in the placement of orthogonality and in how much quadratic-form material closes the term. The textbook selector maps the program’s chapters onto your book’s organization, and drills can be assembled by topic.
Where do students usually need the most practice? Results in this course typically point to rank and nullity, the basis and dimension definitions, and diagonalization — chapters where a definition and a computation must be used together. Chapter-level results in the program show which of these is costing you.
Is linear algebra the same as matrix algebra? Matrix algebra is the course’s opening block — its computational language. Linear algebra is the larger subject: vector spaces, transformations, eigenvalues, and orthogonality, for which matrices are the working representation. The program covers the full course, not only its matrix chapters.
How does this program differ from a calculus program? Entirely in subject: calculus studies change and accumulation; linear algebra studies systems, structure, and transformations. They are separate courses with separate PassProfessor programs, and this program’s scope is the linear algebra syllabus only.
When can I start using the Linear Algebra program? The program is in the works. Join the notify list on this page and we will email you the day it opens.
Disclaimer
PassProfessor is an independent exam-preparation and study provider, based in Salt Lake City, UT and operating entirely online. This program is study preparation only: it is not affiliated with, endorsed by, or sponsored by any textbook publisher, textbook author, college, university, or instructor, and it reproduces no textbook content. Practice questions are original, written to the published structure and standard scope of a linear algebra course; they are not questions from any instructor’s exam or any publisher’s test bank. Your course syllabus is the authority for your course’s schedule, formats, and grading.