Questions: [ left[beginarraylll:l 1 0 3 1 0 1 0 2 2 0 7 2 endarrayright] ] Infinitely many solutions Unique solution No solutions

Solution Steps

To determine the number of solutions of a system of linear equations represented in augmented matrix form, we can use row operations to reduce the matrix to row-echelon form. If we end up with a row of the form [0 0 ... 0 | c] where c is non-zero, then the system has no solutions. If we end up with a row of the form [0 0 ... 0 | 0], then the system has infinitely many solutions. Otherwise, the system has a unique solution.

Perform row operations to reduce the augmented matrix \(A\) to row-echelon form.

The resulting matrix after row operations: \[ \begin{bmatrix} 1 & 0 & 3 & 1 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 0.2 \end{bmatrix} \]

Since the row-echelon form has a row of the form \([0 \, 0 \, 1 \, 0.2]\), the system has \(\boxed{\text{no solutions}}\).

Final Answer