The table below is the row reduction process applied simultaneously to the system of equations, and its associated augmented matrix.
2.
In this example the coefficient matrix has rank 2 while the augmented matrix has rank 3; so this system of equations has no solution.
3.
Using an augmented matrix and an augmented vector, it is possible to represent both the translation and the linear map using a single matrix multiplication.
4.
A system of linear equations is said to be in " row echelon form " if its augmented matrix is in row echelon form.
5.
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.
6.
This row echelon form is the augmented matrix of a system of equations that is equivalent to the given system ( it has exactly the same solutions ).
7.
In practice, one does not usually deal with the systems in terms of equations but instead makes use of the augmented matrix, which is more suitable for computer manipulations.
8.
With respect to an " n "-dimensional matrix, an " n " + 1-dimensional matrix can be described as an augmented matrix.
9.
:If you're solving it by computer, it's called an " augmented matrix ", and there are a number of methods for solving it quickly.
10.
The above-mentioned augmented matrix is called " affine transformation matrix ", or " projective transformation matrix " ( as it can also be used to perform projective transformations ).
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