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Engineering Calculus Notes 242

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

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230 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION (c) ( −→ ı ) = 3, ( −→ ) = 4, parenleftBig −→ k parenrightBig = 5. 2. Is there a linear function : R 3 R for which (1 , 1 , 1) = 0 (1 , 1 , 2) = 1 (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 : R 3 R is linear and (1 , 1 , 1) = 3 (1 , 2 , 0) = 5 (0 , 1 , 2) = 2 then (a) Find ( −→ ı ), ( −→ ), and parenleftBig −→ k parenrightBig . (b) Express ( x,y,z ) as a homogeneous polynomial. (c) Express ( −→ x ) as a matrix multiplication. (d) Express
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