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Theorems from Kernel, image and rank

All theorems from Kernel, image and rank.

[THEOREM]

If $T:V\to W$ is a linear map, then $\ker(T)$ is a subspace of $V$ .

[THEOREM]

If $T:V\to W$ is a linear map, then $\operatorname{im}(T)$ is a subspace of $W$ .

This page builds on Subspaces (Vector spaces), Linear transformations, Basis and dimension (Vector spaces) and Linear independence (Vector spaces).

Part of the thread Kernels and solution sets, in 6 places.

Every solution of $T(x)=b$ is one particular solution plus an element of $\ker T$ .

DFKernelthe kernelALG 3 / Here