A system of three linear equations in three variables looks like: ax+by+czb₁ dx+ey+fz = b₂ gx+hy+iz b3 The matrix representation of this system is: a b d = 2:10-8 JE E e h or, in vector form: Ax = b b₁ where x is the unknown column vector y, b is called the constant column vector b₂ and A is called the coefficient matrix. The determinant of the coefficient matrix A is computed as follows: a b C det(A) or |A| = d e fa(ei-fh) - b(di- fg) + c(dh - eg) lg h Cramer's Rule says that if |A| 0, then the unique solution to this linear system is: (x, y, z) = (BBB) Lb3 where B, is the matrix obtained by replacing column i of A with the constant column b. Sample run #1 This program uses Cramer's Rule to solve a linear system. Enter each of 3 linear equations as four integers separated by space. For example, x-2y + 3z = 4 should be entered as 1 -2 3 4 Enter equation 1: 3 1 Enter equation 2: 2 -1 Enter equation 3: 0 5 2 -1 1 -1 5-5 System has unique solution (0.5, 0.5, -1.5) Sample run # 2 This program uses Cramer's Rule to solve a linear system. Enter each of 3 linear equations as four integers separated by space. For example, x-2y + 3z = 4 should be entered as 1 -2 3 4 Enter equation 1: 2 1 3 14 Enter equation 2: 1 -1 2 7 Enter equation 3: 3 3 4 21 System does not have a unique solution because determinant is 0