Let V = R*. Define f1, f2, f3 € V' by f1(r, y, z) = x – 2y, f2(x, y, z) = x+y+z, and f3(x, y, z) = y – 3z. Prove that (f1, $2, f3) is a lincarly independent list in the dual space, V'. Is it a basis for V'? (why or why not?)

Let V = R*. Define f1, f2, f3 € V' by f1(r, y, z) = x – 2y, f2(x, y, z) = x+y+z, and f3(x, y, z) = y – 3z. Prove that (f1, $2, f3) is a lincarly independent list in the dual space, V'. Is it a basis for V'? (why or why not?)

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*. Define f1, f2, f3 € V' by f1(r, y, z) = x – 2y, f2(x, y, z) = x+y+z, and f3(x, y, z) = y – 3z.
Prove that (f1, $2, f3) is a lincarly independent list in the dual space, V'. Is it a basis for V'? (why or
why not?)

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