Engineering Calculus Notes 242 - 230 CHAPTER 3 REAL-VALUED...

This preview shows page 1. Sign up to view the full content.

View Full Document

230 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION (c) ℓ ( −→ ı ) = 3, ℓ ( −→  ) = 4, ℓ parenleftBig −→ k parenrightBig = − 5. 2. Is there a linear function ℓ : R 3 → R for which ℓ (1 , 1 , 1) = 0 ℓ (1 , − 1 , 2) = 1 ℓ (2 , 0 , 3) = 2? Why or why not? Is there an affine function with these values? If so, give one. Are there others? 3. If ℓ : R 3 → R is linear and ℓ (1 , 1 , 1) = 3 ℓ (1 , 2 , 0) = 5 ℓ (0 , 1 , 2) = 2 then (a) Find ℓ ( −→ ı ), ℓ ( −→  ), and ℓ parenleftBig −→ k parenrightBig . (b) Express ℓ ( x,y,z ) as a homogeneous polynomial. (c) Express ℓ ( −→ x ) as a matrix multiplication. (d) Express