MATH 240
The final exam will cover all the material we have discussed in class and studied in homework this semester, including Sections 7.1 and 7.2.
You should use review sheet 1, review sheet 2 and review sheet 3 to review earlier material.
The following list points out the most important definitions and theorems from Sections 7.1 and 7.2:
Definitions:
- Symmetric matrices
- Quadratic forms
- Classification of quadratic forms
Theorems:
- Theorem 1, 2
- Theorem 4, 5
Important Skills (partial list):
- Decide if a matrix is symmetric.
- Orthogonally diagonalize a symmetric matrix.
- Find the quadratic form associated to a symmetric matrix.
- Find the symmetric matrix associated to a quadratic form.
- Find the change of variable that transforms a given quadratic form into a quadratic form with no cross-product terms.
- Classify a quadratic form as positive definite, negative definite or indefinite.