query: Formal proof for why subtracting two equations in a system of linear equations maintains equivalence with the original system of equations
positive_passages.docid: 147263
positive_passages.text: Why does the elimination method work?
negative_passages.docid: 130498
negative_passages.text: Linear algebra proof regarding matrices
negative_passages.docid: 42427
negative_passages.text: Understanding linear algebra in Ordinary Least Squares derivation
negative_passages.docid: 13899
negative_passages.text: Proof that $-v = (-1)*v$
negative_passages.docid: 131132
negative_passages.text: Proofs using vector properties
negative_passages.docid: 158534
negative_passages.text: Proof that any linear system cannot have exactly 2 solutions.
negative_passages.docid: 83176
negative_passages.text: Writing a system of Linear Equations
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: 47670
negative_passages.text: Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$
negative_passages.docid: 70606
negative_passages.text: Show that the LU decomposition of matrices of the form $\left[\begin{smallmatrix}0& x\\0 & y\end{smallmatrix}\right]$ is not unique
negative_passages.docid: 21578
negative_passages.text: Showing the minimal polynomial for an element in an extension field is the same as the minimal polynomial of a linear transformation.
negative_passages.docid: 150738
negative_passages.text: Proof of $(A - B) - C = A - (B \cup C)$
negative_passages.docid: 2315
negative_passages.text: How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?
negative_passages.docid: 122305
negative_passages.text: Proof of matrix norm property: submultiplicativity
negative_passages.docid: 96748
negative_passages.text: Formal deductions on Hilbert system
negative_passages.docid: 104258
negative_passages.text: Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
negative_passages.docid: 126870
negative_passages.text: Show that axiom of replacement implies from the Axiom of Specification [Proof Verification]