Row operations

Let $ A = \begin{bmatrix}
1 & -2 & 1  0 & 2 & -8  -4 & 5 & 9
\end{bmatrix}$ be a matrix. Then $ [\: 1\: {-2}\:\: 1\:]$, $ [\:0 \:\:2 \:{-8} \:]$, and $ [\:{-4} \:\:5 \:\:9 \:]$ are respectively called the first, the second, and the third row of the matrix $ A$. And $ \begin{bmatrix}1  0  -4 \end{bmatrix}$, $ \begin{bmatrix}-2  2  5 \end{bmatrix}$, and $ \begin{bmatrix}1  -8  9 \end{bmatrix}$ are respectively called the first, the second, and the third column of the matrix $ A$.

Given a matrix $ C$, the following three basic row operations are used to systematically produce a reduced echelon form:

  1. Add a multiple of the $ i$-th row by $ k$ to the $ j$-th row.
  2. Interchange the $ i$-th row and the $ j$-th row.
  3. Multiply the $ i$-th row by $ c$.

Given a matrix C in Matlab/Octave, the above three row operations are carried out as follows:

  1. C(j,:) = C(j,:) + k * C(i,:)
  2. C([j,i],:) = C([i,j],:)
  3. C(i,:) = k * C(i,:)



Department of Mathematics
Last modified: 2005-10-21