Lecture Notes: Determinant of a Square Matrix
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چکیده
j=1 (−1) +j · ai∗j · det(M i∗j). (1) Besides det(A), we may also denote the determinant of A as |A|. Henceforth, if we apply (1) to compute det(A), we say that we expand A by row i∗. It is important to note that the value of det(A) does not depend on the choice of i∗. We omit a proof of this fact, but illustrate it in the following examples. Example 1 (Second-Order Determinants). In general, if A = [aij] is a 2× 2 matrix, then det(A) = a11a22 − a12a21. For instance:
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