Question

non homogeneous system of linear equation Ax=B is consistent if​

Answer 1

Only if the ranking of the coefficients equals the ranking of the augmented matrix, a system of system of equations expressed in matrix form as AX = B is consistent.

The consistency of a homogenous system of linear equations is guaranteed in a matrix.

If the dimensions of the left and right sides of an equation are the same in a matrix , therefore the equation is proved to be dimension valid, according to the homogeneity principle. However, the homogeneity principle fails to provide information about a dimensionless constant of the matrix.