augmented matrix sentence in Hindi
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- For a given number of unknowns, the number of solutions to a system of linear equations depends only on the rank of the augmented matrix is greater than the rank of the coefficient matrix; if, on the other hand, the ranks of these two matrices are equal, the system must have at least one solution.
- For if there are at least as many independent equations as unknowns that will eliminate any stretches of overlap of the equations'surfaces in the geometric space of the unknowns ( aside from possibly a single point ); and if the rank of the augmented matrix exceeds ( necessarily by one if at all ) the rank of the coefficient matrix then the equations jointly contradict each other.
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