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The image space of a linear transformation T:V → W is the set of vectors such that Given the n×n transformation matrix A, the image space of the transformation will be identical to the column space of A. Therefore, because of the rank–nullity theorem, The image space of an invertable (that is, the determinant is not zero) n×n matrix is Rn.

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  • Image space
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  • The image space of a linear transformation T:V → W is the set of vectors such that Given the n×n transformation matrix A, the image space of the transformation will be identical to the column space of A. Therefore, because of the rank–nullity theorem, The image space of an invertable (that is, the determinant is not zero) n×n matrix is Rn.
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  • The image space of a linear transformation T:V → W is the set of vectors such that Given the n×n transformation matrix A, the image space of the transformation will be identical to the column space of A. Therefore, because of the rank–nullity theorem, The image space of an invertable (that is, the determinant is not zero) n×n matrix is Rn.
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