False, the system could also have no solutions, for example if the row directly above the last row has all zeros except for in the last column.

Question

asked 2021-06-23

Determine whether the statement is true or false. If the last row of the reduced row echelon form of the augmented matrix of a system of linear equations has only one nonzero entry, then the system is inconsistent.

asked 2021-05-25

Determine whether the following statement is true or false. If the reduced row echelon form of the augmented matrix of a consistent system of mm linear equations in nn variables contains kk nonzero rows, then its general solution contains kk basic variables.

asked 2021-05-11

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution.

\(\begin{bmatrix}1 & 0&-6 \\1 & 1&3\\ 0 & 0&0\end{bmatrix}\)

asked 2021-06-04

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution.

\(\begin{bmatrix}1 & -2&0 & -4 \\0 & 0&1 & 3\\0 & 0&0 & 0 \end{bmatrix}\)