Solve using matrices.
-x + 7y = -2 3x + y = 34
A) (3, 7)
B) (12, -2)
C) (7, 12)
D) (-2, 3)

Question

Quizplus · Accepted Answer

To solve the system of equations using matrices, we can write the equations in the form AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.A = | 1  7 |    | 3  1 |B = | -2 |    | 34 |To find X, we calculate A^-1 * B.First, find the determinant of A: det(A) = (1)(1) - (7)(3) = 1 - 21 = -20.Then, find the inverse of A (A^-1) by swapping the elements on the main diagonal, changing the signs of the off-diagonal elements, and dividing each term by the determinant:A^-1 = 1/-20 * |  1  -7 |               | -3   1 |A^-1 = | -1/20  7/20 |       |  3/20 -1/20 |Multiplying A^-1 by B gives X:X = A^-1 * B = | -1/20  7/20 | * | -2 |               |  3/20 -1/20 |   | 34 |  = | (1/10) + (7*34)/20 |    | (-3*2)/20 + (-34/20) |  = | (1/10) + (238/20) |    | (-6/20) - (34/20) |  = | 0.1 + 11.9 |    | -0.3 - 1.7 |  = | 12 |    | -2 |Therefore, the solution is X = (12, -2), which corresponds to choice B.

Solve Using Matrices. -X + 7y = -2 3x + Y = 34