Question

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution. Otherwise state that there is no solution.

[1 -5 -4
0 0 7]
A. X1 = - 4 + 5x2 X2 is free
B. (-4,7)
C. X1 = - 4 +5x2
X2=7
X3 is free
D. There is no solution.

Answer 1

Option D (There is no solution) is the correct answer.

Explanation:

According to the question, the matrix is:

⇒
`\left[\begin{array}{ccc}1&-5&-4\\0&0&7\end{array}\right]`

The linear equation will be:

⇒
`x-5y=-4`

and

⇒
`0.x+0.y=7`

i.e,

`0=7` (Not possible)

Thus the above given matrix has no solution. So the above is the correct option.