Question

The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.

Answer 1

Answer:

D

Step-by-step explanation:

Given matrix allows you to write that

$\left\{\begin{array}{r}x\ \ +\ \ 5z=1\\y-3z=4\end{array}\right..$

Let $z=t.$ From the last equation,

$y=4+3z\Rightarrow y=3t+4.$

From the first equation,

$x+5z=1\Rightarrow x=1-5t.$

Then the solution of the system has form

$\left\{\begin{array}{l}x=-5t+1\\y=3t+4\\z=t\end{array}\right.,$

where t is any real number.