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To find the inverse of the matrix \( A = \begin{bmatrix} 3 & 1 & 2 \\ -2 & 3 & -5 \\ 1 & 2 & 4 \end{bmatrix} \) using the Gauss-Jordan method, follow these steps: --- ### Step 1: Augment the matrix with the identity matrix We start by augmenting \( A \) with the identity matrix \( I \): \[ \begin{bmatrix} 3 & 1 & 2 & | & 1 & 0 & 0 \\ -2 & 3 & -5 & | & 0 & 1 & 0 \\ 1 & 2 & 4 & | & 0 & 0 & 1 \end{bmatrix} \] --- ### Step 2: Perform row operations to transform \( A \) into the identity matrix We will perform row operations to convert the left side of the augmented matrix into the identity matrix. The _____ ______ _______ __________ __________ ______ _____ ____ ________ ____ _________ _______.
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