Question

Determine if the linear system

-4x1 + 2x2 = -3
6x2 = 0
First choose which of the following statements are correct.
A. The system is not in echelon form because a variable is the leading variable of two or more equations.
B. The system is not in echelon form because the system is not organized in a descending "stair step" pattern so that the index of the leading variables increases from the top to bottom.
C. The system is not in echelon form because not every equation has a leading variable.
D. The system is in echelon form.
If the system is in echelon form, also identify the leading variables and the free variables.

Answer 1

D option is correct

Leading variables=
`X_1,X_2`

Free variables =none

Explanation:

From the question we are told that

The Equation is

`-4x_1 + 2x_2 = -3`

`6x2 = 0`

The matrix is represented as

`\begin{bmatrix} -4 & 2 & -3 \\0& 6 & 0\\\end{bmatrix}`

This being the matrix form shows the system already in echelon for

Therefore D option is correct

Leading variables=
`x_1,x_2`

Free variables =none