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## Homework Statement

Check the statement is true or false:

Let [itex]\mathcal{A} : \mathbb{R^3}\rightarrow \mathbb{R^4}[/itex] be a linear operator.

If the minimum rank of [itex]\mathcal{A}[/itex] is [itex]2[/itex], than the maximum defect is [itex]1[/itex].

## Homework Equations

-Linear transformations

## The Attempt at a Solution

Assume that [itex]\mathcal{A}[/itex] is a matrix of order [itex]3[/itex]. If the maximum rank of a matrix is two, then number of defects (linearly dependent vectors) is [itex]1[/itex].

Thus, the statement is true.

Is this correct?