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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
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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