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Suppose the augmented matrix for a given system has a pivot in every column. Say as much as you can about the solutions to the corresponding system of equations, with explanation.

User Yurie
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1 Answer

4 votes

Answer:

The system is inconsistent.

Explanation:

Consider the provided information.

The augmented matrix for a given system has a pivot in every column.

Let us understand this fact with the help of an example.

Suppose an 8 × 6 augmented matrix has a pivot in every column.

The above matrix is augmented and has a pivot in every column, that means the rightmost column in the above matrix must be a pivot column.

The rightmost column of the above matrix will be something like this:

0 0 0 0 0 | b

Where b≠0 because if b is 0 then it can't be a pivot position.

But from the above 0 = b, which is false.

This means that the system is not consistent,

Hence, the system is inconsistent.

User Kalthir
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