What is the determinant of a 3x3 matrix?

[Panphobia]

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?

 

[Dick]

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?

Determinants have properties that are related to row operations. Look some of them up. You don't have to explicitly evaluate the determinants.

 

[Panphobia]

Which row operations, I am looking in my textbook and it gives no information on this topic.

 

[Dick]

Which row operations, I am looking in my textbook and it gives no information on this topic.

Ok, try here. http://science.kennesaw.edu/~plaval/math3260/det2.pdf . What happens to the determinant of a matrix when you multiply a row by a constant?

 

[Ray Vickson]

Which row operations, I am looking in my textbook and it gives no information on this topic.

Google is your friend.

 

[Dick]

Google is your friend.

Ack! You revealed my secret. Yes, I typed "row operations determinants" into Google.

 

[Panphobia]

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.

 

[Dick]

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.

Actually, I think I just did "determinant properties". It's not an obscure fact about determinants. Probably in your textbook someplace.

 

[Ray Vickson]

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.

You want to know more about determinants, so Google 'determinant'.