A determinant of second order is made with the elements 0 and 1. Find the number of determinants with non-negative values.

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Solution

In required determinant , each of the four elements can be filled in $2$ ways i.e. by $0$ or $1$ .
So, possible number of determinants $= 2^{4} = 16$

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A determinant of second order is made with the elements 0 and 1. Find the number of determinants with non-negative values.

In required determinant , each of the four elements can be filled in 2 ways i.e. by 0 or 1.So, possible number of determinants =24=16

In required determinant , each of the four elements can be filled in $2$ ways i.e. by $0$ or $1$ .
So, possible number of determinants $= 2^{4} = 16$