Row and column matrix operations

Click For Summary
SUMMARY

The discussion focuses on the operations allowed in matrix manipulation, specifically the mixing of row and column operations. It confirms that while row operations alone may not suffice to achieve a desired matrix form, column operations can be utilized effectively. The rank of the matrix in question is established as 2, indicated by the presence of I2. Additionally, it is clarified that both row and column operations are permissible when calculating the determinant of a matrix.

PREREQUISITES
  • Understanding of matrix rank and its implications
  • Familiarity with row operations in linear algebra
  • Knowledge of column operations in matrix manipulation
  • Basic concepts of determinants in linear algebra
NEXT STEPS
  • Study the properties of matrix rank and its calculation methods
  • Learn about different types of row operations and their applications
  • Explore column operations and their impact on matrix transformations
  • Investigate the calculation of determinants using both row and column operations
USEFUL FOR

Students and professionals in mathematics, particularly those studying linear algebra, matrix theory, and anyone involved in computational mathematics or engineering applications requiring matrix operations.

Shackleford
Messages
1,649
Reaction score
2
Are you allowed to mix and match row and column operations? For (a), using only row operations, I cannot get the matrix into the form they want. Could I swap a few of the columns around to do so?

For (b), I got it into the form they want. The rank of the matrix is 2 because I have I2 there.

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110620_195851.jpg

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110620_210944.jpg

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110620_195802.jpg
 
Last edited by a moderator:
Physics news on Phys.org
You can do column and row operations when finding the determinant.
 

Similar threads

How Do You Find the Inverse of a Non-Square Matrix?
  • · Replies 5 ·
Replies
5
Views
2K
Topology of the Reals: Combining Unions into Single Intervals
  • · Replies 15 ·
Replies
15
Views
3K
Determine is endomorphism, kernel, epimorphism, monomorphism
  • · Replies 5 ·
Replies
5
Views
3K
Proving Find isomorphism: What Else Needed?
  • · Replies 7 ·
Replies
7
Views
2K
Groups and Subgroups: Clarifying Questions
  • · Replies 19 ·
Replies
19
Views
3K
Determining Onto and One-to-One Mappings: Finding Left and Right Inverses
  • · Replies 6 ·
Replies
6
Views
2K
What is distribution function?
  • · Replies 1 ·
Replies
1
Views
1K
What Are the Challenges in Using Tensor Notation for Cartesian Coordinates?
  • · Replies 10 ·
Replies
10
Views
3K
Find Transformation: Tα & Original vs. New Basis
  • · Replies 7 ·
Replies
7
Views
2K
Intermediate analysis homework
  • · Replies 2 ·
Replies
2
Views
2K