IGNOU MTE 4 2018 - Give examples, with justification, of the following:i) two non-zero,

Question

Give examples, with justification, of the following:
i) two non-zero, 3×3 matrices A and B , with | A | = 0, | B| = 5/7i ;
ii) two non-singular 2× 2 matrices C and D , with | C | = sqrt(2) | D| .

02 Feb 2018

Answer :

Word Count : 475

Let's break down the problem step by step. ### i) Two non-zero, 3×3 matrices \( A \) and \( B \) with \( |A| = 0 \) and \( |B| = \frac{5}{7}i \): - A matrix \( A \) with \( |A| = 0 \) is singular, meaning it does not have an inverse, or equivalently, its rows or columns are linearly dependent. - A matrix \( B \) with \( |B| = \frac{5}{7}i \) is a 3×3 matrix with a complex determinant. Example for \( A \) and \( B \): Let: \[ A = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 1 & 2 & 3 \end{pmatrix} \] Here, rows 1

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