the reduced row echelon form of a system of linear equations is given. write the system of equations…

the reduced row echelon form of a system of linear equations is given. write the system of equations corresponding to the given matrix. use w, x, y, and z as variables. determine whether the system is consistent or inconsistent. if it is consistent, give the solution. what equation does the first row represent? (type an equation.)

the reduced row echelon form of a system of linear equations is given. write the system of equations corresponding to the given matrix. use w, x, y, and z as variables. determine whether the system is consistent or inconsistent. if it is consistent, give the solution. what equation does the first row represent? (type an equation.)

Answer

Explanation:

Step1: Recall row - echelon form to equation rule

In an augmented matrix for a system of linear equations, if the matrix is in row - echelon form and the columns correspond to variables (w,x,y,z) (in order) and the right - hand side, each row represents an equation. The first row of the matrix (\left[\begin{array}{cccc|c}1&0&0&9&8\end{array}\right]) means that the coefficient of (w) is 1, the coefficient of (x) is 0, the coefficient of (y) is 0, the coefficient of (z) is 9, and the right - hand side is 8.

Step2: Write the equation

The equation corresponding to the first row is (w + 0x+0y + 9z=8), which simplifies to (w+9z = 8).

Answer:

(w + 9z=8)