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Wawe Shida

Published on July 3, 2014

10-5Properties of Determinants 775 EXAMPLE 1 Taking Out a Common Factor of a Column where 2 is a common factor of the rst column. Matched Problem 1 Take out factors common to any row or any column: EXPLORE-DISCUSS 1 (A)How are and related? (B)How are and related? Theorem 2Row or Column of Zeros If every element in a row (or column) is 0,the value of the determinant is 0. Theorem 2 is an immediate consequence of Theorem 1,and its proof is left as an exercise. It is illustrated in the following example: Theorem 3Interchanging Rows or Columns If two rows (or two columns) of a determinant are interchanged,the new deter- minant is the negative of the original. 3 0 1 2 0 4 5 0 9 0 ka kd kg kb ke kh kc kf ki a d g b e h c f i ka kc kb kd a c b d 3 6 1 2 3 0 1 9 5 6 2 4 1 7 5 3 2 0 2 3 1 2 1 7 5 3 2 0