Meeting 22Determinants and Elementary Operations

The Effects of Elementary RowOperations on a Determinant

Elementary Row Operations and Determinants

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DETERMINANTS AND ELEMENTARY COLUMN OPERATIONS

Although Theorem 3.3 is stated in terms of elementary row operations, the theoremremains valid when the word “column” replaces the word “row.”

Operations performed on the columns (rather than the rows) of a matrix are called elementary column operations.

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MATRICES AND ZERO DETERMINANTS

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Because the second and third rows are multiples of each other, the determinant is zero.

When evaluating a determinant by hand, we sometimes save steps by using elementary row (or column) operations to create a row (or column) having zeros in all but one position and then using cofactor expansion to reduce the order of the matrix by 1.

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Exercises