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Задач{array}.\right.\]1.5.7Systemsofalgebraicequations2.15$Problem:Forthegivenmatrixequationa)solveitbytheGaussmethod,b)makeasubstitutioncheck,c)solving(bytheGaussmethod)theequation\(AX=E\),find\(A^{-1}\),d)checkthecorrectnessoftheanswerbycalculation\(A^{-1}A\),e)solvethegivenequationainusing\(A^{-1}\),comparetheresults.\[A=\left(\begin{array}{cccc}-2&3&-1&0\\2&0&-2&0\\-6&-3&3&0\\0&0&0&-2\end{array}\right),B=\left(\begin{array}{cc}1&-2\\-3&0\\2&-1\\1&-1\end{array}\right),AX=B.\]1.5.8Systemsofalgebraicequations4.31$Problem:Forthegivenmatrixequationa)solveitbytheGaussmethod;b)makeasubstitutioncheck;c)solving(bytheGaussmethod)theequation\(AX=E\),find\(A^{-1}\);d)checkthecorrectnessoftheanswerbycalculation\(A^{-1}A\);e)solvethegivenequationainusing\(A^{-1}\),comparetheresults.\[\begin{aligned}A&=\left(\begin{array}{ccccc}1&4&-2&2&-1\\2&8&-3&2&-2\\2&9&-4&2&-2\\0&-4&2&-1&1\\-1&-1&2&-1&1\end{array}\right),\\B&=\left(\begin{array}{ccccc}3&-1&4&0&1\\5&8&-1&4&2\\1&-2&4&0&1\end{array}\right),\quadAX=B.\end{aligned}\]1.5.9Systemsofalgebraicequations4.31$Problem:1.Findtheangle\(C\)inthetriangle\(ABC\),where\(A=(2;\Gamma;H),B=(3;H;\Gamma),C=(-3;1;\Gamma)\).2.Findtheareaofthetriangle\(ABC\).3.Findthevolumeofthetetrahedron\(ABCD\),where\(\quadA=(1;\Gamma;H),\quadB=(-3;H;\Gamma)\),\(C=(\Gamma;3;-1),D=(2;7;\Gamma)\).Where\(\Gamma=2,H=2\).1.1.3VectorAlgebra2.15$Problem:Calculatethedeterminant\(\left|\begin{array}{lllll}0&1&2&1&1\\1&0&1&0&1\\2&1&0&1&0\\1&1&1&2&1\\1&1&1&1&0\end{array}\right|\).1.2.1Determinantcalculation0.65$Problem:Calculatethedeterminantofthematrixofthe\(n\)-thorder\(a_{jk}=|j-k|\).1.2.2Determinantcalculation4.31$‹1234...115116›mathproblemsbank.netTermsofusePrivacypolicy©2024,MathProblemsBankTrustpilothome.text.login_titlehome.text.login_textClosehome.button.confirm_request_to_solve_taskhome.text.login_titlehome.text.login_textClosehome.button.loginlightbox.option({'resizeDuration':200,'wrapAround':true})(function(m,e,t,r,i,k,a){m[i]=m[i]||function(){(m[i].a=m[i].a||[]).push(arguments)};m[i].l=1*newDate();k=e.createElement(t),a=e.getElementsByTName(t)[0],k.async=1,k.src=r,a.parentNode.insertBefore(k,a)})(window,document,"script","mc.yandex.ru/metrika/t.js","ym");ym(,"init",{clickmap:false,trackLinks:true,accurateTrackBounce:true,webvisor:false});window.fbAsyncInit=function(){FB.init({xfbml:true,version:'v13.0'});};(function(d,s,id){varjs,fjs=d.getElementsByTName(s)[0];if(d.getElementById(id))return;js=d.createElement(s);js.id=id;js.src='connect.facebook.net/ru_RU/sdk/xfbml.customerchat.js';fjs.parentNode.insertBefore(js,fjs);}(document,'script','facebook-jssdk'));