Question

Solve the system of equations by using the inverse of the coefficient matrix of the equivalent matrix equation.

X + 7y = 10
3x + 8y = 4

The inverse of matrix A, A^-1, is

Answer 1

To solve the given system of equations using matrix inversion, express the system in matrix form and then multiply the inverse of the coefficient matrix A by the constants vector B to find the solution vector X.

Step-by-step explanation:

To solve the system of equations by using the inverse of the coefficient matrix of the equivalent matrix equation, we first need to express the equations in matrix form AX = B, where A is the coefficient matrix, X is the vector of variables, and B is the constants vector.

Here are the given equations:

• X + 7Y = 10
• 3X + 8Y = 4

So, we can represent them as:

• A = [[1, 7], [3, 8]]
• X = [X, Y]
• B = [10, 4]

Proceeding with the calculation, we would find the inverse of matrix A (A-1), and then use it to find X by calculating A-1B. Ensure you are capable of performing matrix multiplication and understand the concept of the matrix inverse before you proceed.

Remember to check if the determinant of matrix A is not zero, as only matrices with a non-zero determinant have an inverse.