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ЗадачrocessesMarkovchainsQueuingsystemsTwo-dimensionalrandomvariablesandtheircharacteristicsDefinitionandpropertiesofprobabilityLimittheoremsRealintegralsIntegralsoffunctionsofasinglevariableIndefiniteintegralsDefiniteIntegralsImproperintegralsDoubleintegralsTripleintegralsTheareaofaregionVolumeofasolidVolumeofasolidofrevolutionFluxofthevectorfieldSurfaceintegralsCurvilinearintegralsPotentialandsolenoidalfieldsVectorfieldcirculationIntegralsdependingonaparameterTopologyUSEproblemsVariationalcalculusProblemlistFreeproblemsAttention!Ifasubsectionisselected,thenthesearchwillbeperformedinit!SearchProblem:Findthedecompositionofthevector\(a=(-2;2;2)\)intovectors\(b=(2;1;2)\),\(c=(0;2;-2),d=(1;2;0)\).1.1.1VectorAlgebra0.58$Problem:1.Findthedotproductofvectors\(a=(\Gamma;H;1;\Gamma;2)\)and\(b=(3;\Gamma;2;H;1)\).2.Findtheanglebetweenvectors\(a=(1;H;\Gamma;1;2)\)and\(b=(2;H;\Gamma;3;1)\).3.Findthecrossproductofvectors\(a=(1;H;\Gamma)\)and\(b=(2;H;\Gamma)\).Where\(\Gamma=2,H=2\).1.1.2VectorAlgebra1.95$Problem:Findinversematrixtomatrix\(A\)ofsize\(\timesn\)\[\left(\begin{array}{cccccc}n&n-1&n-2&\ldots&2&1\\1&n-1&n-2&\ldots&2&1\\1&1&n-2&\ldots&2&1\\\ldots&\ldots&\ldots&\ldots&\ldots&\ldots\\1&1&1&\ldots&2&1\\1&1&1&\ldots&1&1\end{array}\right).\]1.4.1Matrixtransformations2.92$Problem:Solvethematrixequation\[AX=B,A=\left(\begin{array}{cc}2&1\\2&-1\end{array}\right),B=\left(\begin{array}{lll}2&1&2\\2&2&1\end{array}\right).\]1.5.1Systemsofalgebraicequations0.58$Problem:Solvethesystemofequations\(\left\{\begin{array}{l}2x+2y=7\\2x-4y=9\end{array}\right.\).1.5.2Systemsofalgebraicequations0.39$Problem:Solvethesystemofequations\[\left\{\begin{array}{c}x_{1}-2x_{2}-2x_{3}+x_{4}=1\\2x_{1}+2x_{2}-x_{3}+x_{4}=1\\x_{1}-x_{2}+x_{3}-2x_{4}=2\end{array}.\right.\]1.5.3Systemsofalgebraicequations0.78$Problem:Solvethematrixequation\(AX=B\),where\[A=\left(\begin{array}{cccc}0&-5&0&-2\\2&1&1&-4\\0&0&-5&-1\\-1&1&-3&2\end{array}\right),B=\left(\begin{array}{c}-2\\-2\\-1\\1\end{array}\right).\]1.5.4Systemsofalgebraicequations1.95$Problem:SolvethematrixequationusingtheGaussmethod:\(AX=B\),where\[A=\left(\begin{array}{ccccc}2&0&-3&15&14\\-2&3&-2&4&1\\-2&2&-4&16&18\\-4&2&-2&5&10\\3&-1&3&-13&-19\end{array}\right),B=\left(\begin{array}{c}19\\17\\16\\0\\-1\end{array}\right)\text{.}\]1.5.5Systemsofalgebraicequations1.95$Problem:Solvethesystemofequations\(\left\{\begin{array}{c}3x-y-z=2\\x+y+z=0\\2x+2y+3z=7\end{array}\right.\)a)Cramer'smethod,b)Gaussmethod,c)Inversematrixmethod.1.5.6Systemsofalgebraicequations1.95$Problem:SolvethesystemofequationsusingtheCramer's,Gaussandinversematrixmethods:\[\left\{\begin{array}{c}x+y-z=2\\2x+y=3\\x-2y+z=0\end{array}.\right.\]1.5.7Systemsofalgebraicequations1.95$Problem:Forthegivenmatrixequationa)solveitbytheGaussmethod,b)makeasubstitutioncheck,c)solving(bytheGaussmethod)theequation\(AX=E\),find\(A^{-1}\),d)checkthecorrectnessoftheanswerbycalculation\(A^{-1}A\),e)solvethegivenequationainusing\(A^{-1}\),comparetheresults.\[A=\left(\begin{array}{cccc}-2&3&-1&0\\2&0&-2&0\\-6&-3&3&0\\0&0&0&-2\end{array}\right),B=\left(\begin{array}{cc}1&-2\\-3&0\\2&-1\\1&-1\end{array}\right),AX=B.\]1.5.8Systemsofalgebraicequations3.9$Problem:Forthegivenmatrixequationa)solveitbytheGaussmethod;b)makeasubstitutioncheck;c)solving(bytheGaussmethod)theequation\(AX=E\),find\(A^{-1}\);d)checkthecorrectnessoftheanswerbycalculation\(A^{-1}A\);e)solvethegivenequationainusing\(A^{-1}\),comparetheresults.\[\begin{aligned}A&=\left(\begin{array}{ccccc}1&4&-2&2&-1\\2&8&-3&2&-2\\2&9&-4&2&-2\\0&-4&2&-1&1\\-1&-1&2&-1&1\end{array}\right),\\B&=\left(\begin{array}{ccccc}3&-1&4&0&1\\5&8&-1&4&2\\1&-2&4&0&1\end{array}\right),\quadAX=B.\end{aligned}\]1.5.9Systemsofalgebraicequations3.9$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\(\Gamma=2,H=2\).1.1.3VectorAlgebra1.95$Problem:Calculatethedeterminant\(\left|\begin{array}{lllll}0&1&2&1&1\\1&0&1&0&1\\2&1&0&1&0\\1&1&1&2&1\\1&1&1&1&0\end{array}\right|\).1.2.1Determinantcalculation0.58$Problem:Calculatethedeterminantofthematrixofthe\(n\)-thorder\(a_{jk}=|j-k|\).1.2.2Determinantcalculation3.9$‹1234...116117›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'});};(funct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