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Unformatted text preview: + (−1)1+n a1n det (A1n ) There are two commonly used notations for the determinant of a matrix A: ‘det(A)’ and ‘|A|’ We have chosen to use the notation det(A) as opposed to |A| because we find that the latter is often confused with absolute value, especially in the context of a 1 × 1 matrix. In the expansion a11 det (A11 ) − a12 det (A12 )+ − . . . +(−1)1+n a1n det (A1n ), the notation ‘+ − . . . +(−1)1+n a1n ’ means that the signs alternate and the final sign is dictated by the sign of the quantity (−1)1+n . Since the entries a11 , a12 and so forth up through a1n comprise the first row of A, we say we are finding the determinant of A by ‘expanding along the first row’. Later in the section, we will develop a formula for det(A) which allows us to find it by expanding along any row. Applying Definition 8.13 to the matrix A = 1 4 −3 2 1 We will talk more about the term ‘recursively’ in Section 9.1. we get 8.5 Determinants and Cramer’s Rule 509 det(A)...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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