Practice question · Multiple choice
Every linear transformation is determined by what it does to the basis vectors. Why is that enough to know its effect on every vector?
Hints
- Write in terms of the basis, then apply and use linearity.
- The two rules of linearity are exactly what is needed.
Show the answer
A. Because any vector is a combination of the basis vectors
Why
Linearity lets the transformation pass through the combination. This is why a matrix IS just the images of the basis vectors written as columns, nothing more is needed.
Practise Linear Transformations
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