2.2 - MATH1850U/2050U: Chapter 2 cont. 1 DETERMINANTS cont....

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MATH1850U/2050U: Chapter 2 cont. .. 1 DETERMINANTS cont. .. Evaluating Determinants by Row Reduction (2.2; pg. 100) Recall: Last day, we introduced the method of cofactor expansion for finding determinants. Today, we will learn to evaluate determinants by row reduction. ..this involves less computations, so it is better for larger matrices. Theorem: Let A be a square matrix. If A has a row of zeroes or a column of zeros, then 0 ) det( A . Example: Theorem: Let A be a square matrix. ) det( ) det( T A A Proof (2x2): Try as an exercise. Proof (3x3): 33 32 31 23 22 21 13 12 11 a a a a a a a a a A 33 23 13 32 22 12 31 21 11 a a a a a a a a a A T The following theorem tells us how elementary row or column operations affect the value of a determinant. Theorem: Let A be an n n matrix. a) If B is the matrix that results when a single row or single column of A is multiplied by a scalar k , then ) det( ) det( A k B b) If B is the matrix that results when two rows or two columns of
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2.2 - MATH1850U/2050U: Chapter 2 cont. 1 DETERMINANTS cont....

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