3.2 Properties of Determinants

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3.2 Properties of Determinants
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REVIEW
Denotation


the submatrix by deleting the ith row and jth
column of A
Example
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REVIEW
Definition For , the determinant
of an matrix is
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REVIEW
Denotation (i, j)-cofactor of A

Theorem 1


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

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Example Compute the determinant
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Theorem 4.


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Example Find the determinant of
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Theorem 5

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Theorem 5

Theorem 6