11/4/2023 0 Comments Matrix inverse adjointSo matrix X is the unknown of the matrix equation. Now, to simplify the following steps, we will name A the square matrix that has the coefficients of the unknowns, X the column matrix with the unknowns, and B the column matrix with the independent terms: We can verify that these matrices correspond to the system of equations by multiplying the matrices, since we would obtain the two equations of the system. Let’s see an example of how to do it:Ī system of equations can be expressed with matrices: Well, one of the applications of the inverse matrix is the resolution of systems of linear equations. Now you may be wondering… what is the inverse matrix for? Is it really used for something? Solving a system of equations with the inverse matrix If a matrix is invertible, the following equation holds for a scalar multiplication:. ![]() The determinant of the inverse of a matrix equals to the reciprocal of the determinant of the original matrix.Transposing a matrix first and then finding the inverse of the matrix is the same as first calculating the inverse of the matrix and then transposing it.The inverse of a matrix multiplication is equal to the product of the inverses of the matrices but changing their order of multiplication.The inverse of the inverse matrix results in the original matrix:.That is, if the matrix is invertible, it only exists one inverse matrix. The inverse matrix has the following characteristics:
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