lets say I have an augmented matrix
$$\begin{bmatrix} 2&0&3\\ 0&1&0\\ 2&1&3 \end{bmatrix}$$
The question is: Is the matrix consistent with a unique solution, inconsistent, or consistent with an infinite solution?
row reducing gives:
$$\begin{bmatrix} 1&0&\frac32\\ 0&1&0\\ 0&0&0 \end{bmatrix}$$
the answer given is: consistent, unique solution.
However, I thought if there is a free variable that indicates infinite solutions? Wouldn't the 3/2 be a free variable?
$\endgroup$ 31 Answer
$\begingroup$Since we are considering an augmented matrix, the related system of equations is
- $2x=3$
- $y=0$
- $2x+y=3$
then the answer is correct, the system is consistent and we have a unique solution.
$\endgroup$ 4
