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I. a) if {x;y,z} is a Imearly indepandant subst of vectors in R", show that {x-Zty, z-ytx, y-X+Z{ Is also Iimcarly indepoandant. IS also R such that b) u,V, and w in {utVi u tw, Vtw} is linearly mdependon Docs this filow thant {u, V,w} is al so linearly Indepandany? are vechers

I. a) if {x;y,z} is a Imearly indepandant subst of vectors in R", show that {x-Zty, z-ytx, y-X+Z{ Is also Iimcarly indepoandant. IS also R such that b) u,V, and w in {utVi u tw, Vtw} is linearly mdependon Docs this filow thant {u, V,w} is al so linearly Indepandany? are vechers

Advanced Engineering Mathematics
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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Some assistance with this algebra question please. It's parts a and b) and I need help on both! Please show as much work as possible, thank you so much

Read and answer He Bilowng aveshns below si |. a) if {xyy,z? is a lmeardy indepandant sulbset t vectors in R", show that {x-Zty, z-ytx, y-X+Z{ Is aiso lincarly indepandant IS also b) u,V, and w are vechors K such that in {utviutw, Vtw} is linearly mdepend ont. Does this follow thart {u,V, w} is al so lincarly Indepundany? HINT. put x-utv, y=utw, za VtW. Than by hypo the ses, I xiy123 is lin. ndep. obsene that and x-2+y=2u and so lrth." mave use of pat a.
Transcribed Image Text:Read and answer He Bilowng aveshns below si |. a) if {xyy,z? is a lmeardy indepandant sulbset t vectors in R", show that {x-Zty, z-ytx, y-X+Z{ Is aiso lincarly indepandant IS also b) u,V, and w are vechors K such that in {utviutw, Vtw} is linearly mdepend ont. Does this follow thart {u,V, w} is al so lincarly Indepundany? HINT. put x-utv, y=utw, za VtW. Than by hypo the ses, I xiy123 is lin. ndep. obsene that and x-2+y=2u and so lrth." mave use of pat a.
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