The maximum and minimum values of (3 × 3) determinant whose elements belong to {0, 1, 2, 3} is

Engineering

Mathematics

Introduction to Determinants

Question

± 9

± 15

± 54

± 32

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$A = |\begin{array}{lll} 0 3 3 \\ 3 0 3 \\ 3 3 0 \end{array}|$ (say)

|A| = 54

$A = |\begin{array}{lll} 3 0 3 \\ 0 3 3 \\ 3 3 0 \end{array}|$

|A| = – 54

∴ Maximum and minimum values of |A| = ± 54

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