Matrices and determinants

Question

If A is an n x n matrix and I is the n x n identity matrix, then the function f(x)=|xI - A| is called the characteristic polynomial of A, and the zeros of f(x) are called the eigenvalues of A. Characteristic polynomials and eigenvalues have many applications. Can someone tell me of such an application? Also, are their applications pertaining to kWh or kW

(kilowatt hour)?

Answer 1

The specific answer depends completely on what your matrix is based on. Matrices are great at solving 'n' different equations of the same number of unknowns. The first thing that I can think of regarding solving matrices is computational fluid mechanics. A simpler example would be something like 'find the number of each candy sold at 3 different stands if each stand sold x, y, z (where xyz are the total price sold at each stand'.

 

A kWhr is indeed a kilo-watt hour, and is a measure of energy. kW is a measure of work (or energy/time). For a matrix problem like this, maybe you could replace the candy in the last example with kWhr of energy produced per day at 3 different power plants using 3 different means of power production.

 

power plant 1 makes 

3 kW from natural gas, 1 kW from petroleum, and 4 kW from solar. etc.

 

I know this is vague, but I hope it helps!