2.3 Proof - Invertible Matrix Thereom

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12 Terms

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I

A is an invertible matrix

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II

A is row-quiv to the nxn matrix

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III

A has n pivot positions

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IV

the equation Ax = 0 only has the trivial solution

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V

the columns of A are linearly independent

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VI

The linear transformation T(x)=Ax is one to one

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VII

The equation Ax=b has at least one solution for every b in R^n

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VIII

The columns of A span R

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IX

The linear transformation T(X) = Ax is onto R^


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X

There is an nxn matrix C such that CA=I


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XI

There is an nxn matrix D such that DA=I

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XII

A^T is inevitable