# Probability that 2x2 matrix of numbers chosen from a set

Suppose that a computer program generates a matrix

Where are chosen randomly from the set {-3, -2, -1, 0, 1, 2, 3}.

What is the probability that the system has a unique solution?

I am fairly certain that this is the case when the determinant is not zero, ie. when

Using a computer script I generated all possibilities and found that the probability of the determinant being zero is so the solution is but I am unsure of how to find this computationally.

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Suppose that a computer program generates a matrix

Where are chosen randomly from the set {-3, -2, -1, 0, 1, 2, 3}.

What is the probability that the system has a unique solution?

I am fairly certain that this is the case when the determinant is not zero, ie. when

Using a computer script I generated all possibilities and ...

#### Solution Summary

The probability that a 2x2 matrix of numbers from a chosen set has a unique solution is determined. A computer script is generated.