Exercise · ZW-LINEAR-TRANSFORMATION-010 · ★★★ Advanced
A linear transformation \(T\) satisfies \(T(1,2)=(0,0)\) and \(T(1,0)=(1,1)\). Compute \(T(0,1)\).
Choose one option.
Show answer
- D. (-1/2, -1/2)
Explanation
Since \((1,2)=(1,0)+2(0,1)\), \(0=T(1,2)=(1,1)+2T(0,1)\), so \(T(0,1)=-\tfrac12(1,1)\).
Review the concept: Linear transformation
A linear transformation \(T\) is a function between vector spaces that preserves addition and scalar multiplication.
\[T(u+v)=T(u)+T(v),\quad T(cu)=cT(u)\]
More practice problems: linear transformation
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