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Let's solve this step by step. ### Part (i): Non-zero 3x3 matrices \( A \) and \( B \) such that: 1. \( |A| = 0 \) 2. \( |B| = \frac{5}{7}i \) #### Solution: 1. Matrix A with \( |A| = 0 \) is a singular matrix. A singular matrix has a determinant of 0, which means its rows or columns are linearly dependent. Example of a 3x3 singular matrix \( A \): \[ A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 1 & 2 & 3 \end{bmatrix} \] - The second row is a multiple of the first row, and the third row is the same as the first. This makes the determinant of matrix \( A \) equal to zero, i.e., \( |A| = 0 \). 2. Matrix B with \( |B| = \frac{5}{7}i \) is a non-singular matrix. Its determinant is a non-zero value. Since the determinant is specified ________ _____ ______ ____ _________ ____ ______ ___ _________ ________ ________.
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