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# Describe the row-echelon form of an augmented matrix that corresponds to a system of linear equations that has an infinite number of solutions.

Forms of linear equations
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asked 2021-05-14
Describe the row-echelon form of an augmented matrix that corresponds to a system of linear equations that has an infinite number of solutions.

## Answers (2)

2021-05-15
If using Gaussian elimination to solve a matrix by writing it in row-echelon form gives a. true statement of @ = 0 in one of the rows, then the system will have infinitely many solutions. A row will correspond to a true statement of 0 = Cif all of the entries in the row are 0s.
For example, the augmented matrix [1,0,0;2,1,0;3,5,0 | 4,6,0] has infinitely many, solutions since the bottom row of 0=0 is a true statement.
2021-08-04
97b
There is a riw consisting of all zeros as shown in example below: [1,0,0;0,1,0;3,5,0 | 3,2,0]

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