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The links below will take you to freely available streaming videos from MIT Open Courseware from the Massachusetts Institute of Technology. Depending on the speed of your internet access, three quality levels are provided.
These are long 40-50 minutes lecture delivered by Professor Gilbert Strang which starts with simple 2x2 matrices, moves on to 3x3 matrices and then beyond. The lecture covers points, lines and planes in 3 dimensions, matrix multiplication and inverse, and a lot more. It is aimed at undergraduate students.

These lectures will give you some idea of how this subject is treated at university level.
The Geometry of Linear Algebra
RM - 56K RM - 80K RM - 220K
Elimination with Matrices
RM - 56K RM - 80K RM - 220K
Multiplication and inverse matrices
RM - 56K RM - 80K RM - 220K
Factorization into A = LU
RM - 56K RM - 80K RM - 220K
Eigenvalues and Eigenvectors
RM - 56K RM - 80K RM - 220K
Linear Transformations and Their Matrices
RM - 56K RM - 80K RM - 220K

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Free lecture notes, exams, and videos are available from Massachusetts Institute of Technology at MIT. No registration required.

Glossary

linear

Straight, not curved. A linear equation is of the first degree, for example y = 2x+1.

matrix

a rectangular or square grid of numbers.

speed

velocity without direction; a scalar quantity

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)FP4Matrix algebraXTRA-
AQA A2 Further Maths 2017Pure MathsExtraMatrix Algebra-
AQA AS/A2 Further Maths 2017Pure MathsExtraMatrix Algebra-
CCEA A-Level (NI)FP1Matrix algebraXTRA-
Edexcel A-Level (UK - Pre-2017)FP3Matrix algebraXTRA-
Edexcel AS Further Maths 2017Further Pure 2ExtraMatrix Algebra - Extra-
Edexcel AS/A2 Further Maths 2017Further Pure 2ExtraMatrix Algebra - Extra-
Methods (UK)M5Matrix algebraXTRA-
OCR A-Level (UK - Pre-2017)FP1Matrix algebraXTRA-
OCR A2 Further Maths 2017Pure CoreExtraMatrix Algebra-
OCR MEI A2 Further Maths 2017Extra PureExtraMatrix Algebra - Extra-
OCR-MEI A-Level (UK - Pre-2017)FP2Matrix algebraXTRA-
Universal (all site questions)MMatrix algebraXTRA-
WJEC A-Level (Wales)FP1Matrix algebraXTRA-