Using elementary transformations, find the inverse of the matrix`[[2, 1],[ 7, 4]]`

Explanation

To find the inverse of the matrix \( A = \begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix} \) using elementary transformations, we will augment the matrix \( A \) with the identity matrix \( I \) and perform row operations to convert \( A \) into \( I \). The augmented matrix will look like this:

\[ \begin{bmatrix} 2 & 1 & | & 1 & 0 \\ 7 & 4 & | & 0 & 1 \end{bmatrix} \]

### Step 1: Make the leading coefficient of the first row equal to 1
To do this, we can divide the first row by 2.
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