Question

Use inverse matrices to find the solution to the system of equations represented by this matrix equation

Answer 1

To solve a system of equations using inverse matrices, represent the system as AX = B, find the inverse of A if it is invertible, and then multiply A-1 by B to get the solution X.

Step-by-step explanation:

In order to find the solution to a system of equations using inverse matrices, you should follow several steps. First, ensure that the system is represented in matrix form as AX = B, where A is the matrix of coefficients, X is the column matrix of unknowns, and B is the column matrix of constants. If the matrix A is invertible (i.e., it has a non-zero determinant), you can find its inverse A-1. The solution to the system is then found by multiplying both sides of the equation by A-1, leading to X = A-1B.

To ensure the accuracy of your solution, it's critical to perform careful checking and rechecking during the algebraic steps. This process will involve finding the determinant, creating the adjoint matrix, and finally multiplying by the reciprocal of the determinant to obtain the inverse. Once the inverse is found, you just multiply it by matrix B to get your unknowns X.

Answer 2

`(1)/(detA)\begin{bmatrix}{d} & {-b} \\ {-c} & {a}\end{bmatrix}`

if you replace it in that order, it should give you the answer

`\begin{bmatrix}{2} & {-3} \\ {-3} & {5}\end{bmatrix}`