coefficient matrix
In mathematics, the coefficient matrix refers to a matrix that contains the coefficients of a system of linear equations
In mathematics, the coefficient matrix refers to a matrix that contains the coefficients of a system of linear equations.
A system of linear equations is a set of equations that can be represented as:
a1x1 + a2x2 + a3x3 + … + anxn = b1
b1x1 + b2x2 + b3x3 + … + bnxn = b2
……
……
……
m1x1 + m2x2 + m3x3 + … + mnxn = bm
Where a1, a2, …, an, b1, b2, …, bm are constants and x1, x2, …, xn are the variables.
The coefficient matrix is a matrix that represents the coefficients of the variables in the system of equations. It is formed by arranging the coefficients in a rectangular grid of rows and columns. Each row represents an equation and each column represents a variable.
For example, consider the following system of linear equations:
2x + 3y = 10
4x – 2y = 6
The coefficient matrix for this system would be:
| 2 3 |
| 4 -2 |
In this case, the coefficient matrix is a 2×2 matrix, where the first row corresponds to the coefficients of x and y in the first equation, and the second row corresponds to the coefficients of x and y in the second equation.
The coefficient matrix is widely used in linear algebra to solve systems of linear equations. By performing various matrix operations, such as row operations or matrix inversion, the coefficient matrix can be manipulated to find the values of the variables x and y that satisfy the system of equations.
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