True

An example would be:

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

where the last row is a false statement since \(0\neq1\)

asked 2021-06-03

Determine whether the statement is true or false. Justify your answer. You cannot write an augmented matrix for a dependent system of linear equations in reduced row-echelon form.

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 2021-05-02

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 2021-05-11

asked 2021-02-09

\(x=at+b , y=ct+d , z=et+f\)

\(2x_1+x_2+x_3=3\)

\(-2x_1+x_2-x_3=1\)