Exercise · ZW-GAUSSIAN-ELIMINATION-009 · ★★★ Advanced
Use elimination to find the rank of \(\begin{pmatrix}1&2&3\\2&4&6\\1&0&1\end{pmatrix}\).
Choose one option.
Show answer
- C. \(2\)
Explanation
\(R_2-2R_1=0\), leaving a zero row; the other two rows are independent, so the rank is \(2\).
Review the concept: Gaussian elimination
Gaussian elimination solves a linear system by reducing its augmented matrix, with coefficients \(A\) and vector \(\mathbf b\), to an echelon form \(U\) using elementary row operations.
\[[A\mid \mathbf b]\ \longrightarrow\ [U\mid \mathbf c]\]
More practice problems: gaussian elimination
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