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# How to Solve Matrices with Variables?

TopA matrix can be defined as an arrangement of Numbers in form of a rectangular array. They contain number of rows and columns. For instance, a matrix having 5 rows and 7 columns will be called as a 5 x 7 matrix. Numbers present in a matrix are called as elements. Any rectangular shape matrix is possible i.e. with 'M' rows and 'N' columns. If M = N, then matrix is considered as a Square matrix. If M = 1, matrix is called as row matrix and for N = 1 it is known as column matrix. A matrix can be of different types like row matrix, column matrix, square matrix, triangular matrix, unity or identity matrix, diagonal matrix, scalar matrix and null matrix. Different types of operations that are possible while solving matrices can be row or column switching, row or Column Addition or subtraction, multiplying rows or columns by a constant factor etc.
Let us take an example to understand how to solve matrices with variables. Suppose we have two Linear Equations given as: 7X + 5Y = 3 and 3X – 2Y = 22
In matrix form these equations can be written as:

Writing the left side of the equation as the product of coefficients and variables matrices:

Next step is to find the inverse of the coefficient matrix. We get the inverse as:
(1 / 7 (-2) – 3 (5)) *

Next, multiply both the sides of the equation 1 by the inverse of
toget

The identity matrix is formed by multiplying the inverse with the original matrix. So, according to the the property of matrices A A-1=I

So final solution for two equations can be given as: X = 4 and Y = -5.