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Rank-Nullity Theorem -- from Wolfram MathWorld

Let V and W be vector spaces over a field F, and let T:V->W be a linear transformation. Assuming the dimension of V is finite, then dim(V)=dim(Ker(T))+dim(Im(T)), where dim(V) is the dimension of V, Ker is the kernel, and Im is the image. Note that dim(Ker(T)) is called the nullity of T and dim(Im(T)) is called the rank of T.



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Rank-Nullity Theorem -- from Wolfram MathWorld

https://mathworld.wolfram.com/Rank-NullityTheorem.html

Let V and W be vector spaces over a field F, and let T:V->W be a linear transformation. Assuming the dimension of V is finite, then dim(V)=dim(Ker(T))+dim(Im(T)), where dim(V) is the dimension of V, Ker is the kernel, and Im is the image. Note that dim(Ker(T)) is called the nullity of T and dim(Im(T)) is called the rank of T.



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https://mathworld.wolfram.com/Rank-NullityTheorem.html

Rank-Nullity Theorem -- from Wolfram MathWorld

Let V and W be vector spaces over a field F, and let T:V->W be a linear transformation. Assuming the dimension of V is finite, then dim(V)=dim(Ker(T))+dim(Im(T)), where dim(V) is the dimension of V, Ker is the kernel, and Im is the image. Note that dim(Ker(T)) is called the nullity of T and dim(Im(T)) is called the rank of T.

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      Rank-Nullity Theorem -- from Wolfram MathWorld
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      Let V and W be vector spaces over a field F, and let T:V->W be a linear transformation. Assuming the dimension of V is finite, then dim(V)=dim(Ker(T))+dim(Im(T)), where dim(V) is the dimension of V, Ker is the kernel, and Im is the image. Note that dim(Ker(T)) is called the nullity of T and dim(Im(T)) is called the rank of T.
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      Let V and W be vector spaces over a field F, and let T:V->W be a linear transformation. Assuming the dimension of V is finite, then dim(V)=dim(Ker(T))+dim(Im(T)), where dim(V) is the dimension of V, Ker is the kernel, and Im is the image. Note that dim(Ker(T)) is called the nullity of T and dim(Im(T)) is called the rank of T.

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      Rank-Nullity Theorem -- from Wolfram MathWorld
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      Let V and W be vector spaces over a field F, and let T:V->W be a linear transformation. Assuming the dimension of V is finite, then dim(V)=dim(Ker(T))+dim(Im(T)), where dim(V) is the dimension of V, Ker is the kernel, and Im is the image. Note that dim(Ker(T)) is called the nullity of T and dim(Im(T)) is called the rank of T.

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      Let V and W be vector spaces over a field F, and let T:V->W be a linear transformation. Assuming the dimension of V is finite, then dim(V)=dim(Ker(T))+dim(Im(T)), where dim(V) is the dimension of V, Ker is the kernel, and Im is the image. Note that dim(Ker(T)) is called the nullity of T and dim(Im(T)) is called the rank of T.
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