Methods of solving linear systems

vector/matrix division is one way to solve a system of linear equations

the vector must have the same number of elements as the number of columns in the square matrix

the division is performed by taking the inverse of the matrix and multiplying it by the vector

to form the inverse matrix, follow these steps

  1. calculate the determinant first, an inverse can only be found if the determinant is not zero
    see how to calculate the determinant ..... HERE
  2. replace each element in the matrix by it's cofactor (minor in determinant form)
    see how to do that ..... HERE
  3. transpose the cofactor array to obtain the adjoint matrix
    find out how to do that ... HERE
  4. multiply the adjoint by the inverse of the determinant and you are done
    view that operation ...... HERE
The final solution vector is obtained by multplying the inverse matrix obtained above by the constant vector
as shown..... HERE

You can see a WORKED EXAMPLE...... HERE

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© copyright 2003 Stephen E. Mendes, Barbados.