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Determin

# Determin -         – – – –...

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How to Calculate Determinants 2X2 ax + by = 0 cx + dy = 0 a b c d = ad - bc (1) 3X3 | | A = a b c d e f g h i (2) Expand in terms of minors of any row or column (pick the row or column with the most zeros). For example, choosing the first column: | | A = a e f h i - d b c h i + g b c e f (3) where you find the appropriate determinant in the expansion by striking out the row and column of the chosen coefficient. These smaller determinants are called minors. For example: | | A = a a b c d | e f g | h i - d a | b c d e f g | h i + g a | b c d | e f g h i (4) Minors have an associated sign, alternating through the matrix:
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Unformatted text preview:         + – + – – + – + + – + – – + – + (5) This is why the second term in equation 3 is negative. We could also have expanded in terms of a row. For example, choosing the second row: | | A = – d       b c h i + e       a c g i – f       a b g h (6) For Larger Matrices: Do the determinant in steps. For example, a 4x4 is expanded in terms of 3x3 determinants and then the 3x3 determinants are expanded in terms of 2x2 determinants....
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