Practice question · Fill in the blanks
Complete the statement with the correct term.
A linear transformation T satisfies T(u + v) = T(u) + T(v) and T(cv) = ______.
Word bank: orthogonal · subspace · unit · cT(v)
Hints
- The two required properties concern sums and scalar multiples.
- Together they say the map commutes with linear combinations.
Show the answer
A linear transformation T satisfies T(u + v) = T(u) + T(v) and T(cv) = cT(v).
Why
These two properties define linearity: preservation of addition and scaling.
Practise Linear Transformations
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