Chapter 11.2, Problem 28AYU

In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use $x,y$; or $x,y,z$; or $x_1,x_2,x_3,x_4$ as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution.

$\left[\begin{array}{c}1\\ 0\\ 0\end{array}\begin{array}{c}0\\ 1\\ 0\end{array}\begin{array}{c}0\\ 0\\ 0\end{array}|\begin{array}{c}0\\ 0\\ 2\end{array}\right]$

To determine

To find: The system of equations corresponding to the given reduced row echelon augmented matrix and find the solution, if possible:

$\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 0\end{array}|\begin{array}{c}0\\ 0\\ 2\end{array}\right)$

Answer to Problem 28AYU

Solution:

No solutions, inconsistent system.

Explanation of Solution

Given:

$\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 0\end{array}|\begin{array}{c}0\\ 0\\ 2\end{array}\right)$

Calculation:

We find that the rank of the coefficient matrix is 2.

The rank of augmented matrix is 3.

Both the ranks are not equal.

Hence the system of equations is inconsistent or has no solutions.