University Linear Algebra Span and Linear Independence — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 2 definitions and 11 theorems, 6 worked examples, 1 diagram, in 11 printable pages. This page lists what the notes cover. The notes themselves come with the University 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.
Span and Linear Independence — 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.
The span of a set of vectors
- Definition — Span
- Theorem — The span is a subspace
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Testing membership in a span
- Theorem — Membership in a span
- Theorem — Membership in polynomial and matrix spaces
- Theorem — Spanning the whole of n-space
Also in this section: 1 worked example, 1 note on method and common errors.
Linear independence in n-space
- Definition — Linear independence
- Theorem — Independence test in n-space
- Theorem — Quick verdicts on independence
Also in this section: 1 worked example, 1 note on method and common errors.
Independence of polynomials, matrices and functions
- Theorem — Independence in polynomial and matrix spaces
- Theorem — Independence of functions
Also in this section: 2 worked examples, 1 note on method and common errors.
Dependence relations and redundant vectors
- Theorem — Dependence and linear combinations
- Theorem — Removing a redundant vector
- Theorem — Row reduction keeps column relations
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 University Linear Algebra Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Span and Linear Independence practice worksheet is free and stays free.
Every University Linear Algebra topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University 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.
Span and Linear Independence practice worksheet About the Span and Linear Independence unit test