Practice question · Fill in the blanks
Complete the description of linear transformations.
The ______ of T is the set of vectors mapped to ______. If the kernel is trivial ({0}), T is ______. The ______ of T is the set of all output vectors.
Word bank: kernel · image · zero · injective · surjective
Hints
- One term names what gets sent to zero, the other what is reached.
- The two together determine injectivity and surjectivity.
Show the answer
The kernel of T is the set of vectors mapped to zero. If the kernel is trivial ({0}), T is injective. The image of T is the set of all output vectors.
Why
Kernel and image characterise the structure of a linear map.
Practise Linear Transformations
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