1
vote
2answers
42 views

How many $3 \times 3$ matrices are singluar?

How many $3 \times 3$ matrices are singluar? Describe the methodology used to achieve the result.
0
votes
0answers
21 views

How to ensure a matrix of a special rank

As described in the subject, how can I ensure a matrix of a special rank. for example, given matrix A of m*n and m>n; Then, how can I mathematically constrain the matrix A to be rank n? As we all ...
0
votes
2answers
54 views

Determining whether the system will have a nontrivial solution?

Say I have a 3x3 matrix (a1 = 3a2 - 2a3), Will they system Ax=b have a nontrivial solution? Is it non-singular? I realize nontrivial means an answer that is not a zero vector. It must be the ...
1
vote
1answer
366 views

Invertibility of a square matrix with zero diagonal elements and positive non-diagonal elements

$M$ is square and $$M(i,j)=0, i=j$$ $$M(i,j)>0, i\ne j$$ Is $M$ full-rank or invertible? Actually the $M$ I am studying has much stronger properties but I guess the simple conditions above might ...
1
vote
1answer
88 views

Invertibility of matrix with each element equal to cofactor

I am doing an exercise book which has one problem that asks you to prove the nonsingularity of a matrix if each element of the matrix equals its cofactor (the determinant submatrix by deleting the ...