What Is the Linear Property of Determinants?

[Winzer]

So I am looking at the proof for this in a linear algebra book and I half way get it:

Theorem:

If the all elements of the jth column of a determinate D are linear combinations of two columns of numbers, i.e., if
$$D=\lambda b_{i}+uc{i}$$ where lambda and mu are fixed numbers, then D is equalto a linear comination of the two determinates:
$$D=D_{1}\lambda+D{2}u$$

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 $$b_{i}$$ wile the jth column of D2 consists of the numbers $$c_{i}$$

 

[Winzer]

Actually I figured it out, sorry for the dumb question.
I have never dealt with any proofs before but I get it.