[Linear algebra] Linear independence problem - I got a different result than the one from the textbook

2021.11.29 14:20 Lastrevio [Linear algebra] Linear independence problem - I got a different result than the one from the textbook

Prove or give a counterexample: If {v1; v2; ... ; vm} is a linearly independent list of vectors in V, then {5v1 - 4v2; v2; v3; ... ; vm} is linearly independent.
(From Axler's "Linear algebra done right" exercise 2.A.7)
The solutions are here. The author proves that the statement is true. But I found a counter example, the set of vectors {(1, 2, 3), (1, 2, 0), (1, 2, 15)} is linearly independent and 5v1 - 4v2 is (1, 2, 15).
So the new set is {(1, 2, 15), (1, 2, 0), (1, 2, 15)} which is obviously not linearly independent. Where's the mistake?
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2021.11.29 14:20 JayPasztor Lopunny 0185 9461 8223

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2021.11.29 14:20 AutoNewspaperAdmin [National] - Small business owners donate to community | CNN

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2021.11.29 14:20 KeysToTheCity33 Roddy Ricch - Dirty (feat A1Beam) (Unreleased)

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2021.11.29 14:20 Fun_Entrepreneur_430 Is there two kinds of Hokk ?

hi people, I bought some of this hokkaido early this year, is there too different kinds off hokkaido? the one I have has a pink background instead of a blue one and its hokkaidu inu instead of hokkaido inu. cheers
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2021.11.29 14:20 eggheadecologist Looks like a FOB for me

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2021.11.29 14:20 Solid_V What is an especially wasteful practice that you've seen rich people do?

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2021.11.29 14:20 breaktheice23 I am almost 23 and never had a boyfriend. Is that normal ?

I will try to keep it short I am a 22 F and I have never had a boyfriend before .I don’t consider myself physically attractive and I am a bit overweight. I have meet couple of people online and we usually click but once we meet in person it seems not to work out. I don’t know if that’s normal? I am starting to question myself If I am enough?
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2021.11.29 14:20 Throwaway5764478 Can nail fungus spread through touching an object?

I just bought a cleaning cloth for my glasses from an optician store. I noticed that the lady had a damaged nail where part of it was black. I suspected that it was nail fungus and so I didn't want to touch it, but I also didn't want to be rude and bought it anyway.

Could it spread to me by surface contact? She did touch the cloth.

If it was fungus then that's absolutely disgusting.
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2021.11.29 14:20 AutoNewspaperAdmin [National] - Firefighters, volunteers, build bikes for kids | CNN

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2021.11.29 14:20 NoPeach7391 My bro in a math problem just now

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2021.11.29 14:20 WallStreetDoesntBet Can ADMP get back in the Covid vaccine picture?

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2021.11.29 14:20 MrArgetlahm Recently returned viking sets off for simple task, ends up building three forts.

First time back playing since my old group collapsed in on itself earlier this year. I still love how I can head off to get core wood to build a bridge, realize that I could use a bridge to get to the core wood, then spend five hours building bridges and forts to get me... to the materials I was going to use to build a bridge. Classic Valheim, right?
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2021.11.29 14:20 solanki7 .

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2021.11.29 14:20 Watercress-Unlucky Saw this beautiful bird at work. Anyone knows what it is? Rio de janeiro, Brazil

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2021.11.29 14:20 DaveWigol Midladder decks be like:

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2021.11.29 14:20 No_Transition2883 fffffff

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2021.11.29 14:20 xxstreakxx Duyrulur

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2021.11.29 14:20 Fair_Confection327 100% P&T but no Update

Spoke with my VSO this morning and I was finally awarded 100% P&T after 98 days in Preparation for Decision. However, it has bounced between Prep for Notification and Pending Decision Approval several times today. Anybody know why?
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2021.11.29 14:20 KingdomPC Should really know better by now.

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2021.11.29 14:20 EmFe01 Louis had so much fun in the snow

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2021.11.29 14:20 Brice978 3 Battery Metal Small-caps to Watch $GEL $EDDY $LIS

3 Battery Metal Small-caps to Watch $GEL $EDDY $LIS The YTD chart for the VanEck Rare Earth Strategic Metals ETF (PSE: REMX) is to your left.

While midrange in returns for the sector, it illustrates the solid growth that illuminates the potential of the three Battery Metal stocks examined below.
The 52-week trade range is USD54.83 to USD120.04.
· Performance over 1-Year: 191.0%
· Expense Ratio: 0.59%
· Annual Dividend Yield: 0.47%
· Assets Under Management: $1.0 billion
· Inception Date: Oct. 27, 2010
“The types of mineral resources used vary by technology. Lithium, nickel, cobalt, manganese, and graphite are crucial to battery performance, longevity, and energy density. Rare earth elements are essential for permanent magnets that are vital for wind turbines and EV motors. Electricity networks need a huge amount of copper and aluminum, with copper being a cornerstone for all electricity-related technologies." (Int'l Energy Agency)
Three Juniors to Watchlist
The global graphite market was valued at USD 14.3 Billion in 2019 and is expected to reach USD 21.6 Billion by 2027, registering a CAGR of 5.3% from 2020 to 2027. Likely a low estimate.
Graphano Energy Ltd. (TSXV: GEL) (FSE: 97G0) (the “Company” or “Graphano Energy“) is a mining company that is focused on evaluating, acquiring, and developing graphite resources with potential—from exploration to production.


The LAB Graphite Property crosses through TIMCAL’s Lac des Iles graphite mine in southern Quebec. That property produces 25,000 tonnes of graphite annually.
Recent results from Graphano’s LAB property show assay results of about 50 (of 190) samples have been received. They are in the range of 0.34% to 23.5% graphitic carbon (Cg) with 19 samples over 10% Cg, 12 samples between 5% and 10% Cg, and the remaining samples with values below 5% Cg. Once all the samples are assessed, the exploration program will be revealed.
The other aspect that should excite investors is that the crossover of the LAB and Timcal deposits bring the ‘Closeology’ benefit to GEL. To review, Closeology benefits a junior mining company by:
· De-risks (or mitigates) smaller plays
· A lot of the exploration already done by large neighbors or predecessors
· Depending on the neighbors, the junior company gets ongoing attention.
· And, of course, the real possibility that the junior will be acquired by a major.
Large flake graphite showings on the property were confirmed with flake size in the range of 0.5 to 5 millimeters, typically present in shear zones at the contact of gneisses and marbles where the graphite content usually ranges from 2% to 20%, based on historical information.
Edison Lithium Metals (TSXV: EDDY) (OTCQB: EDDYF) (FSE: VV0) ("Edison" or the "Company") is a Canadian-based junior mining exploration company focused on procurement, exploration, and development of cobalt, lithium, and other energy metal properties.


The Company’s Lithium properties in Argentina are well placed. The Antofalla Salar is 130 km and five by 20km across. Also 20km from Argentina’s largest producing mine, Livent. It has been publicly stated that Antofalla has the third largest lithium brine reservoir in the world. (Albemarle Corporation).

Eddy acquired Resource Ventures S.A. (ReVe). This Argentinian corporation owns or controls the rights to over 148,000 hectares (365,708 acres) of prospective lithium brine claims in two highly prospective areas in the province of Catamarca, Argentina.
Nathan Rotstein, CEO of Edison, stated;“ReVe’s assets in and around the Antofalla Salar are made up of approximately 107,000 hectares (264,397 acres) of semi-contiguous claims in the northern and southern parts of this salar, offsetting either side of Albermarle's holdings in the center of this salar. This vast block of lithium claims creates what management believes are to be an imposing entry point for EDDY as we enter the burgeoning lithium sector.”
The second area is in the Salar de Pipanaco, a place of early-stage mining. Rotstein further states, "Our claims in the Pipanaco Salar, while only early-stage exploration, may prove to be strategic for a potential regional lithium processing facility located less than 50 km from Catamarca city.”
The mixture of properties with established potential and expected potential feeds into the growth seen to date and into the future. EDDY has robust lithium property acquisition plans.
Lithium South Development Corporation (the "Company") (TSX-V: LIS) (OTCQB: LISMF) (Frankfurt: OGPQ) The Hombre Muerto North Lithium Project is surrounded by two leading lithium producers, Korean giant POSCO and Livent at the northern end of the renowned Hombre Muerto Salar. The NRG-43-101 PEA is available on the site for those who like to go deep.


LIS is testing methods for its Direct Lithium Extraction (DLE) method. Once determined, it will form the basis of production.
Benefits include:
· Reduce production time from months to hours
· Increase the recovery from 42% using traditional extraction to over 80%
· Eliminate the need for large evaporation ponds
· Reduce the environmental footprint of any future production facility
The successful deployment of this technology would be necessary to the industry and particularly LIS shareholders.

Two production wells drilled and cased:

HMN Li Project outlined
· Measured and Indicated Mineral Resources of .57M tonnes Lithium
· Carbonate Equivalent (LCE) and a projected mine life of 30 years.
· A recent Preliminary Economic Assessment returns a Present Net Value of US$ 217 million, CAPEX of US$ 93 million, and an Internal Rate of Return of 30%.
· A Feasibility Study on the project is in progress, including upgrading the current resource to reserve status.
CEO Adrian Hobkirk states, "I personally feel very optimistic that DLE's efficiencies will replace conventional Lithium extraction methods, which are slow as they're dependent upon extracting lithium from ponds via a solar evaporation process."
Bottom Line
The need for Lithium and Graphite for the EV market, in particular, is pretty much accepted by industry and, by extension, investors. While each company has unique favorable characteristics, the commonality is that each subject Company has exceptional properties and potential, and the price appreciation over the last year has been impressive.
Mining methods employed vary, as do the maturity of the properties. What is not in genuine dispute is the need for the graphite and lithium produced by these juniors. Management in each case s well up to the task, and the only decision to make is—with apologies to Lay’s potato chips and its spokesman, the late Bert Lahr:
“Bet you can’t buy just one.”
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2021.11.29 14:20 hydez10 Tampa surgeon in Tesla struck bicycling banker at about 80 mph, records say

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2021.11.29 14:20 heypeanutperson Kalorama Festival in Lisbon

Hey guys, I am from Germany and a huge Arctic Monkeys fan! AM announced last week their festival/concerts schedule for the upcoming summer and a festival called Kalorama also appears in the list. I saw that this is the first of this festival and read on Reddit that it kinda seems fishy since they include some big names in their line up. Do you have any idea of the reliability of the festival? Unfortunately I cannot speak Portugese and I already got the ticket so I feel kinda stressed right now lol.. Thanks a lot!
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2021.11.29 14:20 Canadyans Advice on hiring someone to assist with building the final prototype?

My game is essentially at the point where I'm ready to build and print a final prototype for public testing. It's currently using tiles, tokens and miniatures from other board games, except for the Cards which are custom done through Card Creator.
However, I'm a bit overwhelmed by the need for an illustrator and all of the things need to be done to translate the game to custom parts and get them printed. Do people hire other people to help with that stage of the process? Where would be a good place to start with that? I'm really comfortable with the game design aspect but far less so with the artistic and production aspects of the project.
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