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.
A determinant is a value that is calculated from a square matrix. It represents the scaling factor of the linear transformation described by the matrix.
The determinant of a matrix is calculated using a specific formula depending on the size of the matrix. For a 2x2 matrix, the formula is (ad - bc), and for a 3x3 matrix, it is (a(ei - fh) - b(di - fg) + c(dh - eg)).
The determinant of a matrix is used to solve systems of linear equations, determine the invertibility of a matrix, and calculate the area or volume of shapes in geometry.
The determinant of a matrix affects the properties of the matrix in several ways. For example, if the determinant is 0, the matrix is not invertible. Additionally, the sign of the determinant can determine whether the matrix is orientation-preserving or orientation-reversing.
There are some shortcuts and tricks for calculating determinants, such as using row operations to simplify the matrix or using patterns in the matrix to quickly find the determinant. However, these shortcuts may not always work and it is important to understand the formula for calculating determinants.