# Matrix Problem

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• February 18th 2009, 08:00 PM
ferrarri1500
Matrix Problem
Suppose A is a 3 x n matrix whose columns span R^3. Explain how to construct an n x 2 matrix D such that AD=I3?
• February 18th 2009, 09:30 PM
math2009
$AD\rightarrow 3(\times n \times n) \times 2 \rightarrow 3\times 2 \rightarrow R^{3\times 2},AD=I_3?$, Are you sure ?

$if\ D\in R^{n\times 3},D=[\vec{v}_1,\vec{v}_2,\vec{v}_3], find\ AD=I_3,$
We could do $AD=A[\vec{v}_1,\vec{v}_2,\vec{v}_3]=[A\vec{v}_1,A\vec{v}_2,A\vec{v}_3]=[\vec{e}_1\ \ \vec{e}_2\ \ \vec{e}_3]$
To resolute $A\vec{v}_i=\vec{e}_i$ is easy.