Let `|[3,y],[x,1]|=|[3,2],[4,1]|` Find possible values of x and y if x,y are natural numbers

Explanation

To solve the problem, we need to find the values of \(x\) and \(y\) such that the determinant of the matrix \(\begin{bmatrix} 3 & y \\ x & 1 \end{bmatrix}\) is equal to the determinant of the matrix \(\begin{bmatrix} 3 & 2 \\ 4 & 1 \end{bmatrix}\).

### Step 1: Calculate the determinant of the first matrix
The determinant of a \(2 \times 2\) matrix \(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\) is given by the formula:
\[ \text{det} = ad - bc \]
For the matrix \(\begin{bmatrix} 3 & y \\ x & 1 \end{bmatrix}\):
...