10. Let V = {(x1, x2, x3, x4, x5) ER5: x1 - 2x2 + 3x3x4 + 2x5 (a) Show that S V. = = 0}. {(0, 1, 1, 1, 0)} is a linearly independent subset of (b) Extend S to a basis for V.
10. Let V = {(x1, x2, x3, x4, x5) ER5: x1 - 2x2 + 3x3x4 + 2x5 (a) Show that S V. = = 0}. {(0, 1, 1, 1, 0)} is a linearly independent subset of (b) Extend S to a basis for V.
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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Section 3.4: Number 10
Transcribed Image Text:10. Let
V = {(x1, x2, x3, x4, x5) ЄR5: x1 - +
2x2 3x3
x4 + 2x5
x4 + 2x5 = 0}.
(a) Show that S =
V.
{(0, 1, 1, 1, 0)} is a linearly independent subset of
(b) Extend S to a basis for V.
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