--- ### Question **Determine the rank of the following matrices:** (a) \[ \begin{bmatrix} 1 & 1 \\ 2 & 2 \\ \end{bmatrix} \] (b) \[ \begin{bmatrix} 2 & -2 \\ 1 & 2 \\ \end{bmatrix} \] ### Explanation Matrix (a) is a \(2 \times 2\) matrix with identical columns, suggesting potential linear dependence, which is relevant for determining the rank. Matrix (b) is also a \(2 \times 2\) matrix with different values in each entry, indicating the possibility of both columns being linearly independent. The rank of a matrix is defined as the maximum number of linearly independent column vectors in the matrix, which also equals the number of non-zero rows when the matrix is in row echelon form. ---

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