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 1,2 x + x3,3 - x2} and V = p3(R) (b) L {1,2 + x3,3 - x2,4 - x+ x3} and V = pP3(R) (c) L 1,2x x3,3 - a2,4 - x +x3,2+ x} and V = p3(R) (d) L 1,2 xx3,3- a2,4-xx3,2+ x} and V span (1 -, 3x + a2,3x - a3)
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 1,2 x + x3,3 - x2} and V = p3(R) (b) L {1,2 + x3,3 - x2,4 - x+ x3} and V = pP3(R) (c) L 1,2x x3,3 - a2,4 - x +x3,2+ x} and V = p3(R) (d) L 1,2 xx3,3- a2,4-xx3,2+ x} and V span (1 -, 3x + a2,3x - a3)
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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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 1,2 x + x3,3 - x2} and V = p3(R)
(b) L {1,2 + x3,3 - x2,4 - x+ x3} and V = pP3(R)
(c) L 1,2x x3,3 - a2,4 - x +x3,2+ x} and V = p3(R)
(d) L 1,2 xx3,3- a2,4-xx3,2+ x} and V span (1 -, 3x + a2,3x - a3)
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