If an echelon form of an augmented matrix

conyezere

conyezere

Answered question

2022-06-09

If an echelon form of an augmented matrix for a linear system of equations has a row of the form ([0…0 1| 0]
  , then the system has no solution

True or false (justify) 

Answer & Explanation

madeleinejames20

madeleinejames20

Skilled2023-05-20Added 165 answers

If an echelon form of an augmented matrix for a linear system of equations has a row of the form [001|0], then the system has no solution.
This statement is true and can be justified as follows:
In an echelon form of an augmented matrix, the row of the form [001|0] represents an equation of the form 0x1++0xn1+1xn=0, where x1,,xn are the variables in the system.
This equation can be rewritten as xn=0. In other words, it states that the value of the variable xn is 0.
Since this equation represents a contradiction, stating that xn must be 0, it implies that there is no consistent solution for the system of equations. In other words, the system has no solution.
Therefore, if an echelon form of an augmented matrix has a row of the form [001|0], the statement that the system has no solution is true.

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