Linear Algebra
No. For example, linear algebra, for example, is about linear equations where the domain and range are matrices, not simple numbers. These matrices may themselves contain numbers that are real or complex so that not only is the range not the real numbers, but it is not based on real numbers either.
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.
Matrices are used in pretty much any situation where several linear equations are involved. They're used all over the place in physics, chemistry, engineering, and economics. I linked a site below with more information.
It can be anything that you choose it to be. It can be the whole real line or any proper subset - including disjoint subsets. It can be matrices, all of the same dimensions (Linear Algebra is based on them) or a whole host of other alternatives.
Toshinori Munakata has written: 'Matrices and linear programming with applications' -- subject(s): Linear programming, Matrices 'Solutions manual for Matrices and linear programming'
Inverse matrices are defined only for square matrices.
Linear Algebra
Matrices are tools to solve linear equations. Engineers use matrices in solving electrical problems in circuits using Thevenin's and Norton's theories.
Arthur Cayley
No. For example, linear algebra, for example, is about linear equations where the domain and range are matrices, not simple numbers. These matrices may themselves contain numbers that are real or complex so that not only is the range not the real numbers, but it is not based on real numbers either.
The question contains expressions, not equations. It is not possible to solve linear expressions - whether you use matrices or not.
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.
H. Neill has written: 'Vectors matrices and linear equations'
Charles Gordon Cullen has written: 'Matrices and linear transformations'
Zygmunt Dowgird has written: 'Krakowiany i ich zastosowanie w mechanice budowli' -- subject(s): Algebras, Linear, Linear Algebras, Matrices
Kent Franklin Carlson has written: 'Applications of matrix theory to systems of linear differential equations' -- subject(s): Differential equations, Linear, Linear Differential equations, Matrices