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gruba
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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?