How Do Row Operations Affect a Determinant's Value?

In summary, the conversation discusses evaluating a determinant by expressing the matrix in upper triangular form using row operations. However, the calculator shows a different answer due to an incorrect row operation being performed. The correct value of the determinant is -17.
  • #1
_Bd_
109
0

Homework Statement



Evaluate the following determinant by expressing the matrix in upper triangular form.

Homework Equations



row operations.

The Attempt at a Solution



http://yfrog.com/jnscan0001ugj
http://img707.imageshack.us/img707/6379/scan0001ug.jpg
[PLAIN]http://img707.imageshack.us/img707/6379/scan0001ug.jpg

I want to know what I did wrong there cause I can't figure it out
the calculator shows a different answer.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
In your 4th (or so) step, you replaced row 2 by 1/2 itself. Replacing a row by a nonzero multiple of itself is one row operation that changes the value of the determinant. The other row operation that does this is swapping two rows.

The correct value of the determinant is -17.
 

Related to How Do Row Operations Affect a Determinant's Value?

1. What is a determinant?

A determinant is a value that can be calculated from a square matrix. It is used to determine important properties of the matrix, such as whether it is invertible or singular.

2. How is the determinant of a matrix calculated?

The determinant of a matrix is calculated using a specific formula that involves multiplying and adding elements of the matrix. This formula varies depending on the size of the matrix, but it ultimately involves finding the sum of products of elements along certain diagonal lines in the matrix.

3. What is the significance of the determinant in linear algebra?

The determinant is significant in linear algebra because it provides important information about a matrix. For example, if the determinant is non-zero, then the matrix is invertible, meaning it has a unique solution when solving a system of linear equations.

4. Can the determinant of a matrix be negative?

Yes, the determinant of a matrix can be negative. The sign of the determinant depends on the order in which the elements are multiplied and added according to the determinant formula. A negative determinant indicates that the matrix has been subjected to an odd number of row exchanges during the calculation.

5. Are there any practical applications of determinants?

Yes, determinants have various applications in fields such as physics, engineering, and economics. They are used to solve systems of linear equations, calculate the area of a parallelogram or volume of a parallelepiped, and determine the stretch factor of a transformation matrix, among others.

Similar threads

  • Calculus and Beyond Homework Help
Replies
4
Views
387
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
2K
  • Calculus and Beyond Homework Help
Replies
12
Views
7K
  • Linear and Abstract Algebra
Replies
8
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
679
  • Precalculus Mathematics Homework Help
Replies
32
Views
1K
  • Linear and Abstract Algebra
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
2K
  • Calculus and Beyond Homework Help
Replies
13
Views
2K
Back
Top