Maximum value of a second order determinant whose every element is either 0, 1 or 2 only is :

Engineering

Mathematics

Introduction to Determinants

Properties of Determinant

maximum and minimum of quadratic and rational expression

Question

Maximum value of a second order determinant whose every element is either 0, 1 or 2 only is :

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So, $A = [\begin{array}{cc} a & b \\ c & d \end{array}]$ Given a, b, c & d can only be 0, 1, 2
det A = ad – bc
So for max. value of A,
a = 2 and d = 2 and b, c ε 0, 0
So, Max value of det $A = [\begin{array}{cc} 2 & 0 \\ 0 & 2 \end{array}] = 4$