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If A is a square matrix using from first 10 prime numbers, then the probability that A is a non invertible matrix, is |
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Answer» Answer is (0.019) Let A = \(\begin{bmatrix}a&b\\c&d\end{bmatrix}\) so total number of matrix formed = 104 For non-invertible matrix |A| = ad - bc = 0 ⇒ ad = bc Case I a ≠ d (10 x 9) x 2! Case II a = d 10 x 1 So required probability = \(\frac{10\times9\times2!+10}{10^4}\) = \(\frac{19}{1000}\) = 0.019 |
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