Theorem:

If the all elements of the jth column of a determinate D are linear combinations of two columns of numbers, i.e., if

[tex] D=\lambda b_{i}+uc{i}[/tex] where lambda and mu are fixed numbers, then D is equalto a linear comination of the two determinates:

[tex] D=D_{1}\lambda+D{2}u [/tex]

Here both determinates D1 and D2 have the same columns as the determinate D except for the jth column; the jth colum of D1 consists of the numbers [tex] b_{i}[/tex] wile the jth column of D2 consists of the numbers [tex] c_{i}[/tex]