meeting 22 determinants and elementary operations
TRANSCRIPT
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
