Question

Use an inverse matrix to solve the following system of linear equations: x + 2y = 1, x - 2y = -3?

Answer 1

To solve the system of linear equations using an inverse matrix, you need to write the equations in matrix form, find the inverse of the coefficient matrix, and then multiply it with the constant matrix to find the values of the variables.

Step-by-step explanation:

To solve the given system of linear equations using an inverse matrix, you need to follow these steps:

1. Write the system of equations in matrix form: AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.
2. Find the inverse of matrix A, denoted as A^(-1).
3. Multiply both sides of the equation AX = B by A^(-1) to isolate X: X = A^(-1) * B
4. Calculate the product A^(-1) * B to find the values of x and y.

In this case, the coefficient matrix, A = [[1, 2], [1, -2]], the variable matrix, X = [[x], [y]], and the constant matrix, B = [[1], [-3]].

Calculating the inverse of matrix A:

A^(-1) = (1/6) * [[-2, 2], [-1, 1]]

Multiplying A^(-1) and B:

X = A^(-1) * B = (1/6) * [[-2, 2], [-1, 1]] * [[1], [-3]] = [[1], [-1]]

Therefore, the solution to the system of linear equations is x = 1 and y = -1.