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If a system of three linear equations in three unknowns, which is in the matrix equation form of $A X=D$, is inconsistent, then $\frac{\text { rank of } A}{\text { rank of } A D}$ is
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less than one
We have given a system of linear equations with the three unknowns.
Here, equations are in the matrix form $A X=D$ such that the system is inconsistent.
$\therefore \quad$ Rank of Augmented matrix AD $>$ Rank of coefficient matrix A
Rank of AD > Rank of A
$$
\therefore \quad \frac{\text { Rank of } \mathrm{A}}{\text { Rank of } \mathrm{AD}} < 1
$$
Here, equations are in the matrix form $A X=D$ such that the system is inconsistent.
$\therefore \quad$ Rank of Augmented matrix AD $>$ Rank of coefficient matrix A
Rank of AD > Rank of A
$$
\therefore \quad \frac{\text { Rank of } \mathrm{A}}{\text { Rank of } \mathrm{AD}} < 1
$$
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