Equivalence theorem: there is a pivot position in every row of A.

math.la.t.equiv.row.pivot

Matrix equations and spanning sets

Equivalent statements for a matrix A: for every right-hand side b, the system Ax=b has a solution; every b is a linear combination of the columns of A; the span of the columns of A is maximal; A has a pivot position in every row.

math.la.t.equiv.mat.eqn

math.la.t.equiv.col.span

math.la.t.equiv.row.pivot

math.la.t.mat.eqn.lincomb

Created On: August 25th, 2017; 7 years ago
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