Question

2. Solve the following system using the inverse of a matrix ( 25 pts).

−7x+3y=−29
8x−4y=36

Answer 1

To solve the system of equations -7x + 3y = -29 and 8x - 4y = 36 using the inverse of a matrix, represent the equations in matrix form. Calculate the determinant and adjoint matrix of the coefficient matrix, then multiply the inverse of the coefficient matrix by the constant matrix to find the solution: x = 10 and y = -27.

Step-by-step explanation:

To solve the system of equations -7x + 3y = -29 and 8x - 4y = 36 using the inverse of a matrix, we need to represent the equations in matrix form:

[[-7, 3], [8, -4]] * [[x], [y]] = [[-29], [36]].

To find the inverse of the coefficient matrix, calculate the determinant and then find the adjoint matrix:

determinant = (-7 * -4) - (3 * 8) = 4;

adjoint matrix = [[-4, -3], [-8, -7]].

Finally, multiply the inverse of the coefficient matrix by the constant matrix to find the solution: [[x], [y]] = [[-4, -3], [-8, -7]] * [[-29], [36]].

The solution to the system of equations is x = 10 and y = -27.