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Prove the system equations if A is a 2 x 2 matrix with integer entries.

4. Let A be a 2 x 2 matrix with integer entries. Prove that the system of equations

(a_11)(x_1) + (a_12)(x_2) = b_1

(a_21)(x_1) + (a_22)(x_2) = b_2

has a solution with x_1 and x_2 integers for all integers b_1 and b_2 if and only if D(A_1, A_2) = +/- 1. Interpret this result geometrically.

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This solution is a proof regarding a matrix and the solution of a system of equations provided in an attached Word document.

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