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Author: Tinku Tara

Prove-the-theorem-A-non-empty-subset-W-of-a-vector-space-V-F-is-the-subset-of-V-if-and-only-if-W-1-W-2-W-F-and-W-1-W-2-W-

Question Number 210297 by Spillover last updated on 05/Aug/24 $${Prove}\:{the}\:{theorem}. \\ $$$${A}\:{non}\:{empty}\:{subset}\:{W}\:\:{of}\:{a}\:{vector}\:{space}\:{V}\left({F}\right) \\ $$$${is}\:{the}\:{subset}\:{of}\:{V}\:\:{if}\:\:{and}\:{only}\:{if} \\ $$$$\alpha{W}_{\mathrm{1}} +\beta{W}_{\mathrm{2}} \:\in{W}\:\:\forall\alpha,\beta\:\in\:{F}\:\:{and}\:{W}_{\mathrm{1}} ,{W}_{\mathrm{2}} \:\in{W} \\ $$ Terms of Service…

For-the-given-system-of-simultaneous-linear-equation-2x-1-2x-2-3x-3-4x-4-x-5-0-x-3-2x-4-3x-5-0-x-1-x-2-2x-3-5x-4-2x-5-0-x-1-x-2-2x-3-3x-4-0-a-Write-the-augmented-matrix-and-conve

Question Number 210298 by Spillover last updated on 05/Aug/24 $${For}\:{the}\:{given}\:{system}\:{of}\:{simultaneous}\: \\ $$$${linear}\:{equation} \\ $$$$\mathrm{2}{x}_{\mathrm{1}} −\mathrm{2}{x}_{\mathrm{2}} +\mathrm{3}{x}_{\mathrm{3}} +\mathrm{4}{x}_{\mathrm{4}} −{x}_{\mathrm{5}} =\mathrm{0} \\ $$$$−{x}_{\mathrm{3}} −\mathrm{2}{x}_{\mathrm{4}} +\mathrm{3}{x}_{\mathrm{5}} =\mathrm{0} \\…

Question-210289

Question Number 210289 by Abdullahrussell last updated on 05/Aug/24 Answered by Frix last updated on 05/Aug/24 $$\mathrm{There}'\mathrm{s}\:\mathrm{one}\:\mathrm{number}\:{x}\:\mathrm{with}\:\mathrm{nice}\:\mathrm{properties}: \\ $$$${x}^{\mathrm{2}} ={x}+\mathrm{1},\:{x}^{\mathrm{3}} =\mathrm{2}{x}+\mathrm{1}, \\ $$$$\frac{\mathrm{1}}{{x}}={x}−\mathrm{1},\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\mathrm{2}−{x},\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=\mathrm{2}{x}−\mathrm{1}…

Question-210291

Question Number 210291 by Ismoiljon_008 last updated on 05/Aug/24 Answered by mr W last updated on 06/Aug/24 $${x}=\sqrt{{x}^{\mathrm{2}} }=\sqrt{\mathrm{2}^{\mathrm{2}} +{x}^{\mathrm{2}} −\mathrm{2}^{\mathrm{2}} }=\sqrt{\mathrm{2}^{\mathrm{2}} +\left({x}−\mathrm{2}\right)\left({x}+\mathrm{2}\right)} \\ $$$$=\sqrt{\mathrm{2}^{\mathrm{2}}…