Hello there, can you help me solve a problem? Thank you!Suppose A and B are 2 x 2 matrices. Find a counterexmple to the claim that det(A + B) = det(A) + det(B). The formal definition of the determinant of a square \( n \times n \) matrix \( A \) with entries \( a_{ij} \) and submatrices \( A_{ij} \) defined in the usual way is defined recursively as:\[\text{det}(A) = \sum_{j=1}^{n} (-1)^{i+j} a_{ij} \, \text{det}(A_{ij})\]for any fixed \( i \in \{1, 2, \ldots, n\} \).

Answered: Hello there, can you help me solve a…

Hello there, can you help me solve a problem? Thank you! Suppose A and B are 2 x 2 matrices. Find a counterexmple to the claim that det(A + B) = det(A) + det(B).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Hello there, can you help me solve a problem? Thank you!

Suppose A and B are 2 x 2 matrices. Find a counterexmple to the claim that det(A + B) = det(A) + det(B).

The formal definition of the determinant of a square \( n \times n \) matrix \( A \) with entries \( a_{ij} \) and submatrices \( A_{ij} \) defined in the usual way is defined recursively as:

\[
\text{det}(A) = \sum_{j=1}^{n} (-1)^{i+j} a_{ij} \, \text{det}(A_{ij})
\]

for any fixed \( i \in \{1, 2, \ldots, n\} \).

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Suppose A and B are 2 x 2 matrices. We have to find a counterexample to the claim that det(A + B) = det(A) + det(B).

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