The discussion revolves around finding the determinant of a modified 3x3 matrix based on the properties of determinants and row operations. The original matrix has a known determinant of 5, and participants are exploring how changes to the rows affect the determinant.
Some participants have suggested looking up properties of determinants related to row operations, while others have shared resources for further exploration. There is an acknowledgment of the relationship between row operations and the determinant, but no consensus has been reached on the final answer.
Participants express confusion regarding the lack of information in their textbooks about row operations and determinants, indicating a need for clarification on these concepts.
Panphobia said:Homework Statement
Determinant
|a b c|
|d e f| = 5
|g h i|
What is the determinant of?
|4a 4b 4c|
|3d 3e 3f|
| g h i|
The Attempt at a Solution
So far I got this, a(ei - hf) - b(di - gf) + c(dh - ge) = 5
How would I even go about this, I have 9 unknowns, but only 1 equations?
Panphobia said:Which row operations, I am looking in my textbook and it gives no information on this topic.
Panphobia said:Which row operations, I am looking in my textbook and it gives no information on this topic.
Ray Vickson said:Google is your friend.
Panphobia said:Ohh, so if I factore out the 3 and the 4 I would get 12 det(A) where A is the first matrix, then 12 det(A) = 60, oh ok thanks. And Ray, I wouldn't know what to google.
Panphobia said:Ohh, so if I factore out the 3 and the 4 I would get 12 det(A) where A is the first matrix, then 12 det(A) = 60, oh ok thanks. And Ray, I wouldn't know what to google.