Word Count : 808

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### Solution #### (i) Find the rank of 'A' and 'B' Matrix A: \[ A = \begin{pmatrix} -1 & 1 & 2 \\ 1 & -1 & -2 \\ -2 & 2 & 4 \end{pmatrix} \] - Row Reduction: 1. Add Row 1 to Row 2: \[ \begin{pmatrix} -1 & 1 & 2 \\ 0 & 0 & 0 \\ -2 & 2 & 4 \end{pmatrix} \] 2. Subtract 2 × Row 1 from Row 3: \[ \begin{pmatrix} -1 & 1 & 2 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} \] - The reduced form has 1 non-zero row, so the rank of \( A \) is 1. Matrix B: \[ B = \begin{pmatrix} 1 & 0 & -1 \\ -1 & 1 & 1 \\ 1 & _______ _________ _____ __________ ______.
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