Maximum value of a second order determinant whose every element i… - Vidyadip

Question

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

0
1
2
4

✓

Answer

4

Solution:
So, $\text{A}=\begin{bmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{bmatrix}$
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 $\in$ 0, 0
So, Max value of det $\text{A}=\begin{bmatrix}2&0\\0&2\end{bmatrix}=4$

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