Use the determinant feature of a graphing calculator to solve the system by Cramer's rule . (Round to one decimal place.)
-1.8x + 2.4y - 3.1z = 4.3 4.1x - 7.0y + 1.7z = -4.7
3.0x + 2.6y - 4.4z = -1.8
A) {(27.4, 24.9, 33.8)}
B) {(20.5, 18.7, 25.3)}
C) {(6.8, 6.2, 8.4)}
D) {(13.7, 12.5, 16.9)}

Question

Quizplus · Accepted Answer

The determinant of the coefficient matrix is not zero, so the system has a unique solution. The solution is found by using Cramer's rule, which involves calculating the determinants of three matrices. The determinant of the numerator matrix for x is 43.2, the determinant of the numerator matrix for y is -21.6, and the determinant of the numerator matrix for z is -10.8. The determinant of the coefficient matrix is 12.9. Therefore, the solution is x = 43.2/12.9 = 3.3, y = -21.6/12.9 = -1.7, and z = -10.8/12.9 = -0.8. Rounded to one decimal place, the solution is (3.3, -1.7, -0.8).

Use the Determinant Feature of a Graphing Calculator to Solve