The probability that a randomly chosen 2 × 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to

Step-by-step solution

Let A = [ array ll a & b c & d array ] where a , b , c , d are prime. Total number of matrices A formed =10^4 Let S be a matrix from set of matrices A such that S is singular. For singular matrix | S |= ad - bc =0 ad = bc Number of singular matrices = All entries are same + only two prime number are used in matrix then number of matrices with two prime numbers =(10 9) 2 !=180 then number of matrices with one prime number =10 1=10 So required probability = 10 9 2 !+10 10^4 = 19 1000 =0.019