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Numeracy 2. A function of n variables f(x), where x (I1.....In), is said to be homogeneous of degree k €N if f(tx) = t f(x) for all te R. For each function below, show it is homogeneous (of some degree k) or give an example to show it is not homogeneous. 1. ( ) f(r, y. 2) = Vr + y° + z" 2. (I) f(r, y. z, w) = r²y² + z*w² + xyzw ) f(r, y) = Vr + y². 3. aty 4. (s) f(z, y) = /+)ds %3D

Numeracy 2. A function of n variables f(x), where x (I1.....In), is said to be homogeneous of degree k €N if f(tx) = t f(x) for all te R. For each function below, show it is homogeneous (of some degree k) or give an example to show it is not homogeneous. 1. ( ) f(r, y. 2) = Vr + y° + z" 2. (I) f(r, y. z, w) = r²y² + z*w² + xyzw ) f(r, y) = Vr + y². 3. aty 4. (s) f(z, y) = /+)ds %3D

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 32EQ
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Numeracy 2. A function of n variables f(x), where x (I1.....In), is said to be homogeneous of degree k €N if f(tx) = t f(x) for all t e R. For each function below, show it is homogeneous (of some degree k) or give an example to show it is not homogeneous. 1. ( ) f(r, y.) = Vr + y° + z" ) f(r. y, z, w) = r²y? + z*w² + ryzw ) f(z, y) = Vr + y². 2. (I 3. -») f(z, y) = //?+2+v*\ds 4.
Transcribed Image Text:Numeracy 2. A function of n variables f(x), where x (I1.....In), is said to be homogeneous of degree k €N if f(tx) = t f(x) for all t e R. For each function below, show it is homogeneous (of some degree k) or give an example to show it is not homogeneous. 1. ( ) f(r, y.) = Vr + y° + z" ) f(r. y, z, w) = r²y? + z*w² + ryzw ) f(z, y) = Vr + y². 2. (I 3. -») f(z, y) = //?+2+v*\ds 4.
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