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 ...
$M$ 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 ...
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 ...