query: Prove that $Ax = b$ with complex solution, actually is rational solution
positive_passages.docid: 22192
positive_passages.text: System of linear equations having a real solution has also a rational solution.
negative_passages.docid: 154216
negative_passages.text: Solve $\sin(z) = z$ in complex numbers
negative_passages.docid: 153043
negative_passages.text: Show that $\sqrt{4+2\sqrt{3}}-\sqrt{3}$ is rational using the rational zeros theorem
negative_passages.docid: 106011
negative_passages.text: Proving it has all real roots
negative_passages.docid: 84422
negative_passages.text: $AB=BA$, $AC=CA$ we need to show $BC=CB$
negative_passages.docid: 56612
negative_passages.text: Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
negative_passages.docid: 94037
negative_passages.text: Solving the matrix equation $AP=PB$, where $A$ and $B$ are similar
negative_passages.docid: 121253
negative_passages.text: Prove that any complex matrix can be expressed in term of Hermitian and anti-Hermitian matrices
negative_passages.docid: 140290
negative_passages.text: Solving $AB - BA = C$
negative_passages.docid: 25825
negative_passages.text: Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
negative_passages.docid: 95103
negative_passages.text: A rational matrix such that $A^{2017}=I_n$
negative_passages.docid: 87387
negative_passages.text: Linear equations given by $Ax = b$ have a solution if and only if $\operatorname{rank}(A|b) = \operatorname{rank}(A)$
negative_passages.docid: 38379
negative_passages.text: Showing that $e^z=z$ has infinitely many solutions
negative_passages.docid: 41689
negative_passages.text: Find all solutions: $x^2 + 2y^2 = z^2$
negative_passages.docid: 33469
negative_passages.text: Diophantine equation $ax + by = c$ has an integer solution $x_0, y_0$ if and only if $\gcd(a,b)|c$
negative_passages.docid: 138025
negative_passages.text: How to show the solution of $\dot{x} = Ax $ is an invariant subspace?
negative_passages.docid: 15730
negative_passages.text: Determine the minimum of $a^2 + b^2$ if $a,b\in\mathbb{R}$ are such that $x^4 + ax^3 + bx^2 + ax + 1 = 0$ has at least one real solution