Linear Algebra. Lecture 2

1.

Linear Algebra
Lecture 2
1.7 Linear Independence;
1.8 Introduction to Linear Transformations;
1.9 The Matrix of a Linear Transformation

2.

Learning Objectives:
1. Represent Linear Independence of sets of vectors.
2. To do mapping from R2 to R3.
3. Meaning of shear transformation.
4. Matrix Transformations: Reflections; Contractions and Expansions; Shears.
5. Differentiate onto and one-to-one mapping.

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1.7. Linear Independence

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Solution

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Linear Independence of Matrix Columns

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Sets of One or Two Vectors

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Sets of Two or More Vectors