SOLUTION: |a b c d 1| |b c d a 1| |c d a b 1| =0 |d a b c 1| |b a d c 1|

Algebra ->  College  -> Linear Algebra -> SOLUTION: |a b c d 1| |b c d a 1| |c d a b 1| =0 |d a b c 1| |b a d c 1|       Log On


   

Question 1044576: |a b c d 1|
|b c d a 1|
|c d a b 1| =0
|d a b c 1|
|b a d c 1|

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
.
Perform the following elementary column operations (ECO3) IN SUCCESSION (which don't change the value of the determinant):
1%2AC%5B1%5D+%2B+C%5B4%5D,
1%2AC%5B2%5D+%2B+C%5B4%5D,
1%2AC%5B3%5D+%2B+C%5B4%5D.
What you get is the determinant
.
=,
since columns 4 and 5 have identical entries. (Note that a+b+c+d was factored ONCE only from the fourth column.)