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The system Ax=b is consistent exactly when the vector b lies in the column space of A. Matrix dimensions restrict the possible rank, but the shape of the matrix alone does not guarantee consistency or uniqueness.

Conditions: A is a matrix representing a linear transformation.; b is a vector with compatible dimensions.

The system Ax=b is consistent exactly when the vector b lies in the column space of A. Matrix dimensions restrict the possible rank, but the shape of the matrix alone does not guarantee consistency or uniqueness.

Conditions: A is a matrix representing a linear transformation.; b is a vector with compatible dimensions.