Home/Algebra/Systems of equations/Elementary row operations9. Systems of equationsElementary row operationsLevel: intermedioIn 9. Systems of equationsFormulaCopy LaTeXRi↔Rj; Ri←cRi; Ri←Ri+cRjR_i\leftrightarrow R_j;\;R_i\leftarrow cR_i;\;R_i\leftarrow R_i+cR_jRi↔Rj;Ri←cRi;Ri←Ri+cRjTagsalgebraalgebra formulasystemssystems equationsDetailFoundation of Gaussian and Gauss–Jordan elimination.Explore the ideaComputational complexityShow (CS mode)Found an error? Contact us.Related formulasRelatedRouché–Capelli theoremrank(A)=rank([A∣b])=norrank(A)=rank([A∣b])<norrank(A)≠rank([A∣b])\operatorname{rank}(A)=\operatorname{rank}([A|b])=n \quad\text{or}\quad \operatorname{rank}(A)=\operatorname{rank}([A|b])<n \quad\text{or}\quad \operatorname{rank}(A)\neq\operatorname{rank}([A|b])rank(A)=rank([A∣b])=norrank(A)=rank([A∣b])<norrank(A)=rank([A∣b])Open formulaOpen in sectionRelatedInverse of a 2×2 matrixA−1=1ad−bc(d−b−ca)A^{-1}=\frac1{ad-bc}\begin{pmatrix}d&-b\\-c&a\end{pmatrix}A−1=ad−bc1(d−c−ba)Open formulaOpen in section