query: Proof that If Two Homogeneous System in two unknowns has the same solutions, they are equivalent
positive_passages.docid: 71203
positive_passages.text: Proving that two systems of linear equations are equivalent if they have the same solutions
negative_passages.docid: 114906
negative_passages.text: For $n \in \mathbb{N}$ and $W \leq \mathbb{F}^n$, there exists a homogeneous system of linear equations whose solution space is $W$
negative_passages.docid: 37924
negative_passages.text: Equivalence of norms proof
negative_passages.docid: 153580
negative_passages.text: Solutions of autonomous ODEs are monotonic
negative_passages.docid: 61533
negative_passages.text: Solution af a system of 2 quadratic equations
negative_passages.docid: 14809
negative_passages.text: Existence & uniqueness of solutions of linear congruences $\ cx\equiv b\pmod m$
negative_passages.docid: 62936
negative_passages.text: Proving equivalencies of two versions of the Axiom of Choice
negative_passages.docid: 60140
negative_passages.text: Proof of Equivalence Relation $R=\{(a,b)\in\Bbb N^2: 5\mid (2a+3b)\}$
negative_passages.docid: 146046
negative_passages.text: Are two matrices having the same characteristic and minimal polynomial always similar?
negative_passages.docid: 17363
negative_passages.text: Prove that the intersection of two equivalence relations is an equivalence relation.
negative_passages.docid: 45363
negative_passages.text: Show that both mixed partial derivatives exist at the origin but are not equal
negative_passages.docid: 111122
negative_passages.text: Proof of a theorem in Hilbert's system
negative_passages.docid: 57630
negative_passages.text: Second order homogeneous differential equations: why do repeated roots modify the solution set?
negative_passages.docid: 121765
negative_passages.text: Semigroups and solutions of equation
negative_passages.docid: 40343
negative_passages.text: Solutions of $p!q! = r!$
negative_passages.docid: 103851
negative_passages.text: Show that $\frac{xy}{z} + \frac{xz}{y} + \frac{yz}{x} \geq x+y+z $ by considering homogeneity
negative_passages.docid: 76110
negative_passages.text: Proving that the zero vector is unique