230CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION(c)ℓ(−→ı) = 3,ℓ(−→) = 4,ℓparenleftBig−→kparenrightBig=−5.2. Is there a linear functionℓ:R3→Rfor whichℓ(1,1,1) = 0ℓ(1,−1,2) = 1ℓ(2,0,3) = 2?Why or why not? Is there anaffinefunction with these values? If so,give one. Are there others?3. Ifℓ:R3→Ris linear andℓ(1,1,1) = 3ℓ(1,2,0) = 5ℓ(0,1,2) = 2then(a) Findℓ(−→ı),ℓ(−→), andℓparenleftBig−→kparenrightBig.(b) Expressℓ(x,y,z) as a homogeneous polynomial.(c) Expressℓ(−→x) as a matrix multiplication.(d) Express
This is the end of the preview.
access the rest of the document.