1.6. CROSS PRODUCTS89the row and column containing our entry. ThusA11=. ... a22a23. a32a33A12=. . .a21. a23a31. a33A13=.. .a21a22.a31a32..Now, the 3×3 determinant ofAcan be expressed as thealternatingsumof theentriesof the first row times thedeterminants of their minors:detA=a11detA11−a12detA12+a13detA13=3summationdisplayj=1(−1)1+ja1jdetA1j.For future reference, the numbers multiplying the first-row entries in theformula above are called thecofactorsof these entries: the cofactor ofa1jiscofactor(1j) := (−1)1+jdetA1j.We shall see later that this formula usefully generalizes in several ways.For now, though, we see that, once we have mastered this formula, we can
This is the end of the preview.
access the rest of the document.