CEGEP Linear Algebra The Inverse of a Matrix — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 2 definitions and 6 theorems, 5 worked examples, in 9 printable pages. This page lists what the notes cover. The notes themselves come with the CEGEP Linear Algebra bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
The Inverse of a Matrix — what the notes cover
6 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
What you need
Also in this section: 1 note on method and common errors.
What an inverse is
- Definition — Inverse of a square matrix
- Theorem — An inverse is unique
- Theorem — The inverse of a matrix
Also in this section: 1 worked example, 1 note on method and common errors.
Finding an inverse by row reduction
- Theorem — The augmented-identity method
Also in this section: 1 worked example, 1 note on method and common errors.
Elementary matrices
- Definition — Elementary matrix
- Theorem — Elementary matrices are invertible
Also in this section: 1 worked example, 1 note on method and common errors.
Solving a system with the inverse
- Theorem — The matrix form of a system
Also in this section: 1 worked example, 2 notes on method and common errors.
Conditions equivalent to invertibility
- Theorem — The equivalences
Also in this section: 1 worked example, 1 note on method and common errors.
Where the notes are
The notes are one of the documents in the CEGEP Linear Algebra Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The The Inverse of a Matrix practice worksheet is free and stays free.
Every CEGEP Linear Algebra topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 7 CEGEP Linear Algebra units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.
- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
- Less than the price of one hour of tutoring — for the entire year's solutions
Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.
The Inverse of a Matrix practice worksheet About the The Inverse of a Matrix unit test