Linear property of determinates

  • Thread starter Winzer
  • Start date
598
0
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
[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]
 
598
0
Actually I figured it out, sorry for the dumb question.
I have never dealt with any proofs before but I get it.
 

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