Respuesta :
There are 7 leading elements in the system of seven equations with nine unknowns is in row echelon form, with no trivial (0=0) equations.
Row Echelon Form:
A matrix is in Row Echelon form if it has the following properties:
- Any row consisting entirely of 0 occurs at the bottom of the matrix.
- For each row that does not contain entirely zeros, the first non-zero entry is 1. It is called as leading 1.
- For two successive non-zero rows, the leading 1 in the higher row is further left than the leading one in the lower row.
For reduced row echelon form, the leading 1 of every row contains 0 below and above its in that column.
Given,
Suppose that a system of seven equations with nine unknowns is in row echelon form, with no trivial (0=0) equations.
Here we need to find the number of leading variables.
Since we have
number of equations = 7
number of unknowns = 9
So, the row echelon for of the matrix is
=> 7 x 9
Based on this, we understand that, at most 7 leading variables.
Because in in each row there is at least one leading variable.
So, there are 7 leading variables.
To know more about Row Echelon Method here.
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