MAT 2401 Linear Algebra 4.5 Basis and Dimension

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Presentation transcript:

MAT 2401 Linear Algebra 4.5 Basis and Dimension

HW Written Homework

Exam 2 Please study for the exam. Review Lab Solutions. Review written HW solutions. The details in the Keys are the minimum expectations. Resolve any questions you may have.

Preview

Questions What is the “size” of a vector space? Is R 2 “smaller” than R 3 ? Why? Is R 2 “smaller” than P 2 ? Why?

Answers To answer these questions, we need to look into a few things… Linear Combination Spanning Set Linear Independence Basis (4.5) Dimension (4.5)

Prototype R n

What is so special about S ?

Prototype R n

Spanning Set

Basis

Example 1

Remarks

Example 2

Example 3 is the standard basis for M 2,2.

Fact #1

Fact #2

Dimension of a Vector Space

Example 6

Solon? What’s up?