1. 3.2 Properties of Determinants

2. REVIEW
Denotation
: the submatrix by deleting the ith row and jth column of A
Example:

3. REVIEW
Definition
For , the determinant of an matrix is

4. REVIEW
Denotation:
(i, j)-cofactor of A :
Theorem 1

5. REVIEW
Theorem 2
If A is a triangular matrix, then det A is the product of the entries
on the main diagonal of A.

6. Theorem 3
Row Operations
Let A be a square matrix.
If a mutiple of one row of A is added to another row to produce a matrix B, then det B=det A.
If two rows of A are interchanged to produce B, then det B= - det A.
If one row of A is mutiplied by k to produce B, then det B=k det A.

7. Example: Compute the determinant

8. Theorem 4.

9. Example: Find the determinant of

10. Theorem 5

11. Theorem 5
Theorem 6