Using elementary transformations, find the inverse of each of the matrices`[[3 ,10],[ 2, 7]]`

Explanation

To find the inverse of the matrix \( A = \begin{pmatrix} 3 & 10 \\ 2 & 7 \end{pmatrix} \) using elementary transformations, we will augment the matrix \( A \) with the identity matrix \( I \) and perform row operations to transform \( A \) into \( I \). The augmented matrix will look like this:

\[ \begin{pmatrix} 3 & 10 & | & 1 & 0 \\ 2 & 7 & | & 0 & 1 \end{pmatrix} \]

### Step 1: Make the leading coefficient of the first row equal to 1
To do this, we can divide the first row by 3:
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