meeting 22 determinants and elementary operations
TRANSCRIPT
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Meeting 22Determinants and Elementary Operations
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The Effects of Elementary RowOperations on a Determinant
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Elementary Row Operations and Determinants
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Example
Solusi:
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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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Example
Solusi:
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MATRICES AND ZERO DETERMINANTS
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Example
Solusi:
Because the second and third rows are multiples of each other, the determinant is zero.
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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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Example
Solusi:
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Example
Solusi:
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Exercises
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