Math 220BC CONCEPT REVIEW SHEET

1. Write the exact definition(s) for the concept. Learn the definition(s) word for word.

a. Linear independence

b. Linear dependence

2. Add equivalent description(s) (in your own words). (Theorem 7)

3. Copy important theorem(s) word-for-word.

4. Provide examples and counterexamples (Figures 1-4, Exercises 9-20, 33-38)

5. Sketch some geometric interpretations. (Figures 1, 2 and 4)

6. Identify special cases. (Theorems 8,9, box p. 67, Examples 3,5,6)

7. Summarize algorithms or typical computations. (Examples 1,2, Exercises 1-8)

8. Describe connections with other concepts (Box on p. 66, Examples 2,4, Exercises 27, 30, 39 )

9. Add additional examples, situations, or connections as you encounter them:

Linearly independent applies to a set of vectors, not to a single vector, nor to equations nor to a matrix.
Columns of a matrix may be linearly independent, but the matrix is not.
A set of vectors may not have a non-trivial solution -- only equations have solutions.