Instructor: Prof. Gilbert StrangThis course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.Find more lecture notes, study materials, and more courses at http://ocw.mit.edu.This course corresponds to Spring 2011's dictation.

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Introduction

Example: Ax = b

Solvability: Condition on b

Does the system have a solution?

What's the sequence of steps to find the solution?

How do I find one particular solution?

How do I find the rest?

The complete solution

Plot all solution

Where are my solutions?

What's our definition of rank?

Full column rank

Full row rank

Full rank
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Introduction

Example 1 in R^2

Example 2 in R^2

Example 3 in R^2

Linear independence in R^2

Linear independence in R^n

Rank of the matrix

Span a space

Span the column space

Basis for a vector space

Examples of a basis in R^3

What's the requirement on that matrix?

Example in R^2 and R^3

Introduction to dimension space

Dimension space

Example of dimension space
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