Let V=R? and let (R?)* be the dual space for R².Subtask (a).Find the basis {¢1, ¢2} that is dual to the following basis of R?: {vi=(2, -2,), V2=(0, 4)}.Subtask (b).Find the basis {v1, v2} of R² that is dual to the basis {01, ¢2} of (R²)* defined byф1(х, у)- з х+4y;ф2(х, у)-зх;

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Let V=R? and let (R?)* be the dual space for R². Subtask (a). Find the basis {d1, þ2} that is dual to the following basis of R?: {vi=( 2, -2,), V=(0, 4)}. Subtask (b). Find the basis {V1, V2} of R² that is dual to the basis {01, 02} of (R²?)* defined by ф1 (х, у)- з х+4,y; ф2(х, у)-з.х;

Let V=R? and let (R?)* be the dual space for R². Subtask (a). Find the basis {d1, þ2} that is dual to the following basis of R?: {vi=( 2, -2,), V=(0, 4)}. Subtask (b). Find the basis {V1, V2} of R² that is dual to the basis {01, 02} of (R²?)* defined by ф1 (х, у)- з х+4,y; ф2(х, у)-з.х;

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 (R?)* be the dual space for R².
Subtask (a).
Find the basis {¢1, ¢2} that is dual to the following basis of R?: {vi=(2, -2,), V2=(0, 4)}.
Subtask (b).
Find the basis {v1, v2} of R² that is dual to the basis {01, ¢2} of (R²)* defined by
ф1(х, у)- з х+4y;
ф2(х, у)-зх;

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