While the area of a triangle can conveniently be calculated when the triangle is a right triangle, more complicated angles might mean a more complicated calculation of area. If the lengths of the sides of the triangle are unknown, then the problem can still be solved through matrices and determinants. This method typically involves using the simple form of Cramer’s Rule, although it can also be applied to problems requiring the extended version (as in, a 3-by-3 matrix) using that rule.
More applicable to engineering than any other area of study, matrices can be used to solve circuit problems involving input/output voltages. This usually involves a simple 2-by-2 matrix calculation. To solve these problems, one must also know the components of the circuit (resistors, operational amplifiers, capacitors etc.), along with the input voltage. Currents and output voltages can then be discovered mathematically through a properly set up matrix function.
Matrices are not just applicable to engineers and mathematicians, however. Business analysts and planners should also have a basic knowledge of matrices when working with pricing and marketing analysis. The form of matrices used for this type of calculation depends upon the analysis being done and can easily range anywhere from a 3-by-4 matrix to a much larger rectangular matrix. For all sizes, however, the marketing analysis is still performed the same, just on a larger or smaller scale.
Matrices are used regularly for all forms of coding; this includes both computer programming and cryptology. For computer programming, two dimensional arrays are used to include the information needed from the relevant matrices. When coding messages, the particular message sent is obviously dependent upon the code for the matrix behind the message system. Whoever is on the receiving end of the coded message must know the original matrix that it is based on in order to accurately decipher the message.