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(d) If w E R" then the function fw : R" R defined by fw (v) =v•w for all v E R" is a linear form. %3D (f) If A E Mn(R) is invertible then so is the bilinear form f(v, w) = v" Aw. *(g) If Ex : P2 →R is the evaluation map defined by Ex(f) = f(x) then E1+E2 = E3. %3D %3D 3,5 Show that if we regard Cn as a vector

(d) If w E R" then the function fw : R" R defined by fw (v) =v•w for all v E R" is a linear form. %3D (f) If A E Mn(R) is invertible then so is the bilinear form f(v, w) = v" Aw. *(g) If Ex : P2 →R is the evaluation map defined by Ex(f) = f(x) then E1+E2 = E3. %3D %3D 3,5 Show that if we regard Cn as a vector

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(d) If w E R" then the function fy : R" R defined by fw(v)=v•w for all v E R" is a linear form. *( (f) If A E Mn(R) is invertible then so is the bilinear form f(v, w) = v' Aw. *(g) If Ex : P2 R is the evaluation map defined by E-(f) = f(x) then E1 +E2 = E3. %3D %3D 1.3.5 Show that if we regard Cn as a vector
Transcribed Image Text:(d) If w E R" then the function fy : R" R defined by fw(v)=v•w for all v E R" is a linear form. *( (f) If A E Mn(R) is invertible then so is the bilinear form f(v, w) = v' Aw. *(g) If Ex : P2 R is the evaluation map defined by E-(f) = f(x) then E1 +E2 = E3. %3D %3D 1.3.5 Show that if we regard Cn as a vector
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