By means of a finite sequence of elementary row operations, called Gaussian elimination, any matrix can be transformed to row echelon form.
12.
The dimensional matrix as written above is in reduced row echelon form, so one can read off a kernel vector within a multiplicative constant:
13.
Using these operations, a matrix can always be transformed into an upper triangular matrix, and in fact one that is in row echelon form.
14.
The dimensional matrix as written above is in reduced row echelon form, so one can read off a kernel vector to within a multiplicative constant:
15.
A system of linear equations is said to be in " row echelon form " if its augmented matrix is in row echelon form.
16.
A system of linear equations is said to be in " row echelon form " if its augmented matrix is in row echelon form.
17.
These results may be easier to understand by putting the augmented matrix of the coefficients of the system in row echelon form by using Gaussian elimination.
18.
Unlike the row echelon form, the reduced row echelon form of a matrix is unique and does not depend on the algorithm used to compute it.
19.
Unlike the row echelon form, the reduced row echelon form of a matrix is unique and does not depend on the algorithm used to compute it.
20.
If we instead put the matrix " A " into reduced row echelon form, then the resulting basis for the row space is uniquely determined.
