How Many 3x3 Non-Singular Matrices Exist with Four 1s and Five 0s?

  • Context: MHB 
  • Thread starter Thread starter juantheron
  • Start date Start date
  • Tags Tags
    Matrices
Click For Summary
SUMMARY

The discussion focuses on calculating the number of 3x3 non-singular matrices containing four entries of 1 and five entries of 0. It is established that to find the count of non-singular matrices, one should first determine the total number of possible matrices and then subtract the number of singular matrices. This approach ensures an accurate count of non-singular configurations.

PREREQUISITES
  • Understanding of matrix theory and properties of singular vs. non-singular matrices
  • Familiarity with combinatorial counting techniques
  • Knowledge of 3x3 matrix structure and entry configurations
  • Basic understanding of linear algebra concepts
NEXT STEPS
  • Research combinatorial methods for counting matrix configurations
  • Learn about the properties of singular matrices in linear algebra
  • Explore the concept of matrix rank and its implications for non-singularity
  • Study examples of non-singular matrices and their applications in various fields
USEFUL FOR

Mathematicians, students studying linear algebra, and anyone interested in combinatorial matrix theory will benefit from this discussion.

juantheron
Messages
243
Reaction score
1
The no. of $3 \times 3$ non - singular matrices matrices, with four entries as $1$ and all other entries as $0$
 
Physics news on Phys.org
jacks said:
The no. of $3 \times 3$ non - singular matrices matrices, with four entries as $1$ and all other entries as $0$
I assume the question is "Find the number of ...", in which case I suggest you count the number of ways you can make a singular matrix and then subtract this from the total number of all possible matrices.
 

Similar threads

Undergrad Basis of 2x2 matrices with real entries
  • · Replies 11 ·
Replies
11
Views
6K
MHB Could you prove that f(A)>=0 whenever A>0?
  • · Replies 6 ·
Replies
6
Views
1K
Undergrad Congruence for Symmetric and non-Symmetric Matrices for Quadratic Form
  • · Replies 7 ·
Replies
7
Views
2K
MHB Set is closed as for multiplication of matrices
  • · Replies 16 ·
Replies
16
Views
2K
Undergrad Spectral theorem for Hermitian matrices-- special cases
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad 3x3 Diagonalizable Matrices over GF(2)
  • · Replies 31 ·
2
Replies
31
Views
6K
MHB Find Eigenvalues of 4x4 Matrix with -1 & 3 Entries
  • · Replies 8 ·
Replies
8
Views
3K
MHB Understanding One-Sided Ideals in Mathematics
  • · Replies 5 ·
Replies
5
Views
2K
MHB Symmetric and anti-symmetric matrices
  • · Replies 2 ·
Replies
2
Views
2K
Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?
  • · Replies 2 ·
Replies
2
Views
2K