2. Elementary row operations
Elementary row operations are the following transformations:
These operations do not change the solution set of a linear system.
2.1 Example: solving by elimination
x + 2y − z = 1, 2x + 5y + z = 4, −x − y + 2z = 0.
Clarum for macOS · v0.1.0
The calmest way to read and understand Markdown.
Clarum brings navigation, search, categories, and technical rendering into one focused macOS reading space.
Clarum viewer
The entire reading surface is the Clarum product experience.
Reader Preferences
Choose the page tone before you settle in.
Clarum keeps profile, typography, and layout choices local to the reader, so Markdown stays untouched while the page feels right for the session.
- Eight curated canvases cover neutral, paper, academic, and dark reading modes.
- Default Neutral remains compatibility-safe and visibly selected.
- Typography and layout controls sit below the profile chooser, just like the app popover.
Reader Preferences
Profiles shape the page tone; typography and layout stay local to this reader.
Reading profileChoose a curated canvas tuned for long-form Markdown.
- Local Markdown
- Read-only workflow
- Reader preferences
- Category organization
- Technical rendering
- PDF export
Why Clarum
Treat Markdown as knowledge to read, not files to manage.
Clarum connects the core flow of reading, organizing, and understanding local documents without adding unnecessary noise.
Structure appears the moment you open a file
Content, table of contents, search, and sidebar context sit together so long Markdown files feel navigable.
Original files stay untouched
Clarum focuses on displaying local files. Sidebar organization and aliases act as a reading layer inside the app.
Built for technical notes
Tables, math, code, and Mermaid diagrams are treated as first-class parts of the reading experience.
Mac-native interaction flow
Multi-selection, context menus, sidebar groups, and toolbar actions follow patterns Mac users already understand.
Product strengths
Core Clarum strengths through product views
Each section shows where Clarum reduces friction and strengthens the reading experience.
A sidebar that gets stronger as files grow
Group documents by subjects like Linear Algebra or Real Analysis. The library reflects learning flows and project units instead of acting like a flat file list.
- Subject-based document groups
- Document count badges
- Uncategorized items remain visible
Select multiple documents and organize them at once
Use multi-selection and a context menu to move selected documents into a category, export PDFs, or remove items from the sidebar view.
- Batch category movement
- PDF export for selected documents
- Sidebar-only removal for safer cleanup
Diagrams read like part of the document
Mermaid flowcharts render directly inside Markdown, keeping concept maps and processes in the same reading context as the surrounding text.
- Flowcharts and concept maps
- Helpful for math and development notes
- Stays inside the document context
Know which local documents are still available
When a file is moved or missing, Clarum makes that state clear in the sidebar so the reading library stays understandable.
- Missing-file state display
- Readable local library status
- Original-file-preserving flow
Local promise
Clarum is a tool for reading local files.
Clarum is not a remote service. It focuses on helping you read the Markdown files you already have, organize them safely in the sidebar, and export rendered PDFs when needed.
Read-only focusOriginal files preservedNative macOS flow
Clarum for macOS · v0.1.0
Turn scattered Markdown into a library you want to read.
A calm macOS Markdown viewer for long notes, math documents, research material, and developer references.