Definition of Kernel and Range of a Linear Transformation and when is a Linear Transformation one to one and onto. Please note, In example 1(a), the point is (0,-3,-3). Sorry for the typing error.
We form an augmented matrix [A:B] by writing all the coefficients of LHS and RHS and then use Gauss elimination method and reduce the matrix to REF form . In the question here we reduced to REF form the last row has all zeros which means system is solvable . When the rank of A = rank of [A:B] we say system is solvable
