(Proof-verification) Prove that a consistent linear system Ax = b has infinitely many solutions if and only if Ax = 0 has a nontrivial solution
120186
Consistent linear system
27248
If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
64731
Determine $"a"$ for which the system has no solutions, infinitely many solutions, or has one solution
62816
Proof that ODE solutions with Wronskian identically zero are linearly dependent
31898
Sufficient conditions for $x, Ax, A^2x, ...$ being linearly indepedent
29078
find all the values of a and b so that the system has a) no solution b) 1 solution c) exactly 3 solutions and 4) infinitely many solutions
51483
Prove: If a linear map, $φ: U→V$ is bijective, then $φ(x)=0$ has only the solution $x=0$.
24837
$x^2+1=0$ uncountable many solutions
71203
Proving that two systems of linear equations are equivalent if they have the same solutions
35066
Nature and number of solutions to $xy=x+y$
110116
Newton's method linear convergence proof
113407
Finding all solutions for a system of equations with constraint on the sum of absolute values
130498
Linear algebra proof regarding matrices
98298
Prove that bilinear form can be presented as product of linear forms if and only if it has rank one
110408
Solving for $A$ in $Ax = b$
81879
$Av=λv$ basis proof problems
55210
Prove that the equation: $c_0+c_1x+\ldots+c_nx^n=0$ has a real solution between 0 and 1.