Exercise · ZW-GAUSSIAN-ELIMINATION-003 · ★☆☆ Basic
In the augmented matrix \(\begin{pmatrix}1&2&5\\2&3&8\end{pmatrix}\), apply \(R_2\leftarrow R_2-2R_1\). What is the new row 2?
Choose one option.
Show answer
- B. \((0,\,-1,\,-2)\)
Explanation
\((2,3,8)-2(1,2,5)=(0,-1,-2)\). Adding instead of subtracting would give \((4,7,18)\).
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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- ZW-GAUSSIAN-ELIMINATION-006 After elimination, a system has the row (0\ \ 0\ \ |\ \ 4). What can you conclude?
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- ZW-GAUSSIAN-ELIMINATION-009 Use elimination to find the rank of [1 2 3; 2 4 6; 1 0 1].