The row space is the vector space spanned by the row vectors of A.
To find a basis for the row space
Matrices + Row Basis
, row basis:
You can find other bases by choosing Reduced Row Echelon Form from the Matrices submenu, or by applying Fraction-Free Gaussian Elimination and then taking the nonzero rows from the result.
Matrices + Reduced Row Echelon Form
, row echelon form:
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The preceding calculation gives the same basis as found in the previous example.
Matrices + Fraction-free Gaussian Elimination
, fraction-free Gaussian elimination:
The nonzero rows in the preceding matrix give a basis for the row space: