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Finding a Minor and its Complementary Minor

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Let \( A = [a_{ij}] \) be a 5-square matrix, and let \( I = \{1, 2, 4\} \) and \( J = \{2, 3, 5\} \). Then \( I' = \{3, 5\} \) and \( J' = \{1, 4\} \), and the corresponding minor \( |M| \) and complementary minor \( |M'| \) are as follows:
linear-algebradeterminantsminorssubmatricescomplementary-minorsmatrix-entriesindex-setsmatrix-theory

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What this problem tests

Tests the ability to correctly identify and extract submatrices given sets of row and column indices.

This is a foundational example in linear algebra, often used before introducing Laplace's expansion of determinants.

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