Appendix 7

Matrix Algebra Revision

The solution of the second-order matrix

is a₁ b₂ − a₂ b₁.

The solution of the third-order matrix

is

a₁, a₂, . . ., c₂, c₃ are called the elements of the matrix.

The lower order matrix associated with a₁, that is

is called the cofactor of a₁, denoted A₁. Similarly,

is the cofactor of b₁, denoted B₁, and so on. Thus the solution of the third order matrix is

a₁A₁ + b₁B₁ + c₁C₁

and so on for higher orders.

To get the cofactor signs correct, think of the element positions in the matrix as having positive and negative signs associated with them, as follows:

Matrix multiplication