Lec 10 - RREF and Rank
Wednesday, January 25, 2012
A system of linear equations is homogeneous if the RHS contains only zeros.
The only solution of
Thus the set is linearly independent.
The solution set has vector equation
The rank of a matrix is the number of leading ones in the RREF of the matrix.
First, is the set linear independent?
Note that every homogeneous system is consistent.
If there is an infinite number of solutions, let
Be the homogeneous system.
Apply the Subspace Test:
The solution set is non-empty since the system is consistent.
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