For the given lists L and vector spaces V, use basic dimension arguments to say what you | can about L. Is it linearly independent? Does L span V? (If there is no nice dimension argument, just write "requires computation" for full credit.) (a) L {1,2x3,3 - a2} and V p3(R) 1,2 x, - a2,4 - x 3} and V = p3(R). (b) L (c) L {1,2 x x3,3- 2,4 - x + x3, 2+x} and V = p3(R) 1,2 x3,-x2,4 -x+x3,2+ x} and V = span (1 - x, 3x x2, 3x - 3) |(d) L
For the given lists L and vector spaces V, use basic dimension arguments to say what you | can about L. Is it linearly independent? Does L span V? (If there is no nice dimension argument, just write "requires computation" for full credit.) (a) L {1,2x3,3 - a2} and V p3(R) 1,2 x, - a2,4 - x 3} and V = p3(R). (b) L (c) L {1,2 x x3,3- 2,4 - x + x3, 2+x} and V = p3(R) 1,2 x3,-x2,4 -x+x3,2+ x} and V = span (1 - x, 3x x2, 3x - 3) |(d) L
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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Only part d please.
Transcribed Image Text:For the given lists L and vector spaces V, use basic dimension arguments to say what you
| can about L. Is it linearly independent? Does L span V? (If there is no nice dimension
argument, just write "requires computation" for full credit.)
(a) L {1,2x3,3 - a2} and V p3(R)
1,2 x, - a2,4 - x 3} and V = p3(R).
(b) L
(c) L {1,2 x x3,3- 2,4 - x + x3, 2+x} and V = p3(R)
1,2 x3,-x2,4 -x+x3,2+ x} and V = span (1 - x, 3x x2, 3x - 3)
|(d) L
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