Solution of Linear Equations Study Notes for Mechanical and Civil Engineering Exams

1.   System of Linear Equations:

1.1 Homogenous System of Linear Equations:

If the system of m homogeneous linear equations in n variables x₁, x₂, …. x_n is given by:

Then, the set of these equations can be written in matrix form as AX = O

where A is matrix of the coefficients and X is the column matrix of the variables.

1.2 Non – homogenous system of linear equations:

If the system of ‘m’ non-homogeneous linear equation in ‘n’ variables x₁, x₂, … x_n is given by

Then, the set of these equations can be written in matrix form as:

     AX = B    ……… (2)

Where A is coefficient matrix, X is column matrix of the variables and B is the column matrix of constants b₁, b₂, …. b_n.

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