Why the discriminant of a system of linear equation=0 implies it has infinity many solution?
61359
Set of Linear equation has no solution or unique solution or infinite solution?
20034
Does $a^2+b^2=1$ have infinitely many solutions for $a,b\in\mathbb{Q}$?
39993
Count the number of positive solutions for a linear diophantine equation
4443
Why is the determinant zero iff the column vectors are linearly dependent?
10926
System of Linear Equations - how many solutions?
34206
Quadratic form under $\mathbb{C}$ finite-dimension vector space always have a nonzero vector that yields zero?
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
36998
In $Ax=b$. If $A$ is not invertible there are no solutions or infinity. How to determine what the case is?
52621
Why is $\det(A - \lambda I)$ zero?
64662
Classification of a linear system of equations with a parameter
121358
What is the exact relation between a full rank matrix and its determinant?
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
157269
If $\alpha_{1},\ldots,\alpha_{m}$ are vectors different from zero vector, then there is a linear functional $f$ such that $f(\alpha_{i})\neq 0$
28148
Are there any simple ways to see that $e^z-z=0$ has infinitely many solutions?
44354
Total number of solutions of an equation
68323
Using Vieta's theorem for cubic equations to derive the cubic discriminant
1751
When does the tensor product distribute over an infinite direct product?