100.

FALSE

An example would be:

\(\begin{bmatrix}1 & 0&1&:&3 \\0 & 1&2&:&7\\0 &0 &0&:&0\end{bmatrix}\)

Which is in reduced row-echlomn form & has infinitely many solutions since 0=0 is a true statement.

asked 2021-06-28

Determine whether the statement is true or false. Justify your answer. When using Gaussian elimination to solve a system of linear equations, you may conclude that the system is inconsistent before you complete the process of rewriting the augmented matrix in row-echelon form.

asked 2021-05-02

Determine whether the statement is true or false. If the last row of the reduced row echelon form of an augmented matrix of a system of linear equations has only zero entries, then the system has infinitely many solutions.

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 2021-05-27

Determine whether the following statement is true or false. A system of linear equations Ax=b has the same solutions as the system of linear equations Rx=c, where [R c] is the reduced row echelon form of [A b].

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.

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