A determinant is chosen at random from the set ofall determinant of order 2 with elements 0 or 1 only. Find the probabilitythat the determinant chosen is nonzero.

A determinant is chosen at random from the set ofall determinant of or

1.	A determinant is chosen at random from the set ofall determinant of order 2 with elements 0 or 1 only. Find the probabilitythat the determinant chosen is nonzero.
Answer» Determinant `Delta` of order 2 will be of the form `\|(a, b),(c,d)\|`. `therefore Delta = ad - bc` The total number of ways of choosing a, b, c and d is `2 xx 2 xx 2 xx 2 = 16` Now, `Delta ne 0` if and only if either ad = 1, bc = 0 or ad = 0, bc = 1. For ad = 1, (a,d) -= (1, 1). For bc = 0, (b, c) -= (0, 1), (1, 0), (0, 0). So, three cases are there. Similarly, for ad = 0 and bc = 1, there will be three cases. `therefore` Number of favourable cases = 3 + 3 = 6 So, required probability = `(6)/(16) = (3)/(8)`

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A determinant is chosen at random from the set ofall determinant of order 2 with elements 0 or 1 only. Find the probabilitythat the determinant chosen is nonzero.

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