An introduction to matrix algebra
John J. Bird, Carl T.F. Ross · 2019
Matrices are used to solve problems in statics, quantum mechanics, electronics, optimisation, genetics, and much more. In computer graphics, matrices are used to project a three-dimensional image on to a two-dimensional screen, and to create realistic motion. A matrix in its most usual form is an array of scalar quantities arranged as a rectangular table of m rows and n columns. This compact method of representing scalar quantities allows matrices to be particularly suitable for analysing complicated physical problems with the aid of computers. The minor of an element of a 3 by 3 matrix is the value of the 2 by 2 determinant obtained by covering up the row and column containing that element. In the main, matrices and determinants are used to solve a system of simultaneous linear equations. The simultaneous solution of multiple equations finds its way into many common engineering problems; in fact, modern structural engineering analysis techniques are all about solving systems of equations simultaneously.