Let V=R? and let (R²)* be the dual space for R?.Find the basis {o1, 02} that is dual to the following basis of R?: {vi=(2, -2.), v2=(0, 2 )}.Find the basis {V1, V2} of R? that is dual to the basis {01, 02} of (R?)* defined byd1(x, y)=2 x+2y;02(x, y)=2x;

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Let V=R? and let (R?)* be the dual space for R?. Find the basis {oı, 02} that is dual to the following basis of R?: {v=(2,-2.), v2=(0, 2 )}. Find the basis {V1, V2} of R² that is dual to the basis {01, 02} of (R²)* defined by d1(x, y)=2 x+2y: (x, y)=2x;

Let V=R? and let (R?)* be the dual space for R?. Find the basis {oı, 02} that is dual to the following basis of R?: {v=(2,-2.), v2=(0, 2 )}. Find the basis {V1, V2} of R² that is dual to the basis {01, 02} of (R²)* defined by d1(x, y)=2 x+2y: (x, y)=2x;

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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Question

Let V=R? and let (R²)* be the dual space for R?.
Find the basis {o1, 02} that is dual to the following basis of R?: {vi=(2, -2.), v2=(0, 2 )}.
Find the basis {V1, V2} of R? that is dual to the basis {01, 02} of (R?)* defined by
d1(x, y)=2 x+2y;
02(x, y)=2x;

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