Coefficient Matrix

Introduction for Matrix:

A matrix is a rectangular array or arrangement of entries or elements displayed in rows and columns put within a square bracket or parenthesis. The entries or elements may be any kind of numbers (real or complex), polynomials or other expressions. Matrices are denoted by the capital letters like A, B, C…

A = [ai, j] m * n

i, j represent the numbers of m, n.

i, j, m, n all represented in the suffix of the considered terms.

A = `[[a11,b12],[c21,d22]]`

order of above matrix 2 * 2

Definition for Coefficient matrix:


The coefficient matrix is formed from the linear equations. There can be any number of linear equations. In the linear equation we are taking the coefficient of the variables in the linear equation to forms the coefficient matrix. Consider  linear equation from it we are going to form a coefficient matrix. The general linear equation as follows:

a11x1 + a12x2 + . . . +a1nxn = b1
a21 x1 + a22x2 + . . . +a2nxn = b2
a31x1 + a32x2 + . . . +a3nxn = b3
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
am1x1 + am2x2 + . . . +amnxn = bn

The coefficient matrix for the linear equation will be represented as:

A = `[[a11,a12,. . .,a1n],[a21,a22,. . .,a2n],[a31,a32,. . .,a3n],[.,.,. . .,.],[am1,am2,. . .,amn]]`

m * n

The coefficient matrix is formed from the linear equations.

Order or size of a coefficient matrix:

The order or size of number of Row Matrix and the number of columns that are present in a matrix.


Example for coefficient matrix:


The coefficient matrix is a resultant from the linear equations.

Linear equation as follows as:

x + 2y +3z = 4
2x + 3y + 4z = 5
3x + 4y +5z = 6

The coefficient equation of the above linear equation as follows:

A = `[[1,2,3],[2,3,4],[3,4,5]]`
3 * 3

The coefficient matrix is formed from the set of linear equations.