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3.2 Properties of Determinants

3.2 Properties of Determinants. Denotation. REVIEW. : the submatrix by deleting the i th row and j th column of A. Example:. Definition For , the determinant of an matrix is. REVIEW. REVIEW. Denotation:

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3.2 Properties of Determinants

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  1. 3.2 Properties of Determinants

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

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

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

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

  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

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