The inverse of addition is subtraction.
Please clarify what you want to "solve". There are several operations you can do with matrices, such as add them, multiply them, transpose them, etc.
Gauss Elimination
No. Determinants are only defined for square matrices.No. Determinants are only defined for square matrices.
The multiplicative inverse, or reciprocal, of a number "x", is "1/x". For example, the multiplicative inverse of 5 is 1/5. For a fraction, just exchange numerator and denominator. For example, the multiplicative inverse of 2/5 is 5/2.
Matrices are tools to solve linear equations. Engineers use matrices in solving electrical problems in circuits using Thevenin's and Norton's theories.
The inverse of addition is subtraction.
Please clarify what you want to "solve". There are several operations you can do with matrices, such as add them, multiply them, transpose them, etc.
Matrices are generally used to solve simultaneous equations. You use the co-efficient of the variables and arrange them in a matrix to solve them. To do so requires at least as many equation as there are variables. Other uses include vector calculations.
The question contains expressions, not equations. It is not possible to solve linear expressions - whether you use matrices or not.
Gauss Elimination
Addition and subtraction are inverse operations. So you can solve addition by subtracting.
The most common use for inverted matrices is to solve a set of simultaneous equations.
No. Determinants are only defined for square matrices.No. Determinants are only defined for square matrices.
The multiplicative inverse, or reciprocal, of a number "x", is "1/x". For example, the multiplicative inverse of 5 is 1/5. For a fraction, just exchange numerator and denominator. For example, the multiplicative inverse of 2/5 is 5/2.
Given a function, one can "switch" the variables x and y and then solve for y afterwards to determine the inverse function.
It isn't clear what you want to solve for. If you want to find the matrix, there is not a unique solution - there are infinitely many matrices with the same determinant.