Matrices can be used for circuit analysis because a circuit component can have an impedance matrix, an admittance matrix or a scattering matrix, of order equal to the number of ports the circuit has. This can also be used for antenna arrays when you have an antenna circuit connected to a feeder (transmission-line) circuit.
Matrices are also used in the numerical solution of linear equations: when you have a system of N equations it needs matrices of order N.
In field theory integral equations arise which can be solved numerically by using a piecewise-linear approximation which turns an integral equation into a set of linear equations. This is used for analysing raio antennas using the method of moments.
All the above applications are coded into software which can be bought and used but designing the sotware falls inside the remit of electrical engineering.
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Matrices have a wider application in engineering. Many problems can be transformed in to simultaneous equation and their solution can easily be find with the help of matrices.
Vector calculus is applied in electrical engineering especially with the use of electromagnetics. It is also applied in fluid dynamics, as well as statics.
Matrices are a vital mathematical tool for calculating forces, vectors, tensions, masses, loads and a myriad of other factors that must be accounted for in engineering to ensure a safe and resource-efficient structure.
Unless your "everyday life" involves work in some area of engineering, you won't use matrices in your everyday life.
If you have a system, which can be expressed as a set of linear equations, then you can utilize matrices to help solve it. One example is an electrical circuit which uses linear devices (example are constant voltage sources and resistive loads). To find the current through each device, a set of linear equations is derived.