query: If the matrix $A$ that is $m\times n$, has a colum that has only zeros then $Ax=0$ Has infinite solutions.
positive_passages.docid: 27248
positive_passages.text: If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
negative_passages.docid: 112428
negative_passages.text: Existence of least squares solution to $Ax=b$
negative_passages.docid: 139740
negative_passages.text: The infinite product of the sines of all positive integers is zero
negative_passages.docid: 35631
negative_passages.text: $H_0(X,A) = 0 \iff A \cap X_i \neq \emptyset \forall $ path-components $X_i$
negative_passages.docid: 52564
negative_passages.text: $m\times n$ matrix with an even number of 1s in each row and column
negative_passages.docid: 131972
negative_passages.text: All nilpotent $2 \times 2$ matrices satisfy $A^{2}=0$
negative_passages.docid: 56102
negative_passages.text: Prove that there is no non-zero linear operator on $\mathbb C^{2}$ such that $(\alpha | T\alpha) = 0$
negative_passages.docid: 41411
negative_passages.text: How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$
negative_passages.docid: 32458
negative_passages.text: Does the rank-nullity theorem hold for infinite dimensional $V$?
negative_passages.docid: 64731
negative_passages.text: Determine $"a"$ for which the system has no solutions, infinitely many solutions, or has one solution
negative_passages.docid: 31326
negative_passages.text: Number of $(0,1)$ $m\times n$ matrices with no empty rows or columns
negative_passages.docid: 52208
negative_passages.text: Show that a matrix $A$ is singular if and only if $0$ is an eigenvalue.
negative_passages.docid: 74441
negative_passages.text: Zero divisors in matrix rings
negative_passages.docid: 140252
negative_passages.text: Matrices - Conditions for $AB+BA=0$
negative_passages.docid: 124090
negative_passages.text: zero matrix to the power of 0
negative_passages.docid: 124505
negative_passages.text: Proof that there must exist infinitely many solutions to a homogeneous system of equations when more unknowns than equations
negative_passages.docid: 102707
negative_passages.text: Why square matrix with zero determinant have non trivial solution