If the entries in a $3 \times 3$ determinant are either $0$ or $1,$ then the greatest value of their determinant is

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

9

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $2$
Given : $△ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣$
Using 'Sarrus' rule :
$△ = [a_{1} b_{2} c_{3} + b_{1} c_{2} a_{3} + c_{1} a_{2} b_{3}] - [a_{3} b_{2} c_{1} + b_{3} c_{2} a_{1} + c_{3} a_{2} b_{1}]$
For $Δ$ to be maximum, $[a_{3} b_{2} c_{1} + b_{3} c_{2} a_{1} + c_{3} a_{2} b_{1}] = 0$
$\Rightarrow a_{1} = b_{2} = c_{3} = 0$
$∴ Δ = b_{1} c_{2} a_{3} + c_{1} a_{2} b_{3}$
It will be maximum, when $a_{2} = a_{3} = b_{3} = b_{1} = c_{1} = c_{2} = 1$
$∴ Δ_{max} = 2$

Suggest Corrections

Similar questions

Q. If the entries in a

3 \times 3

determinant are either

0

or 1, then the greatest value of their determinats is:

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability).