Question
Give examples, with justification, of the following:
i) two non-zero, 3×3 matrices A and B , with A| = 0 |B| = 5/7 i;
ii) two non-singular 2× 2 matrices C and D , with |C| = √2| D |.
Answer :
Word Count : 640
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 ___ __________ ____ ________ _____ __________.
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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 ___ __________ ____ ________ _____ __________.
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