Prova de Introdução à Álgebra Linear - Subespaços Vetoriais, Interseção e Bases

UNIVERSIDADE FEDERAL DA PARAÍBA CCEN DEPARTAMENTO DE MATEMÁTICA INTRODUÇÃO A ÀLGEBRA LINEARREMOTA Assis Primeira avaliação presencial 20212 AlunoaMatrí Questão 1 1 Defina subespaço vetorial e usando tal definição determine quais dos seguintes conjuntos abaixo são subespaços vetoriais 2 Vetores da forma x 0 0 do ℝ3 3 Todas as matrizes 2 x 2 com entradas inteiras 4 Todos os polinômios 𝑝𝑥 𝑎0 𝑎1𝑥 𝑎2𝑥2 𝑎3𝑥3 para os quais 𝑎0 0 Questão 2 Determine um vetor do ℝ3 que gere a interseção entre U 𝑥 𝑦 0 𝑐𝑜𝑚 𝑥 𝑦 ℝ e W 1231 11 Questão 3 Seja 1 1 1 2 4 1 1 0 3 2 2 1 uma base para o espaço das matizes simétricas Encontre o vetor das coordenadas da matriz A 1 5 5 5 em relação a base Questão 4 Sejam U 𝑥 𝑦 𝑧 𝑡 𝑦 2𝑧 𝑡 0 e W 𝑥 𝑦 𝑧 𝑡 𝑥 𝑡 𝑒 𝑦 2𝑧 1 Determine uma base e a dimensão de U W e U 𝑊 2 Determine se ℝ4 𝑈 𝑊 𝐽𝑢𝑠𝑡𝑖𝑓𝑖𝑞𝑢𝑒 𝑠𝑢𝑎 𝑟𝑒𝑠𝑝𝑜𝑠𝑡𝑎 Questão 5 1 Defina base de um espaço vetorial 2 Segundo sua definição os conjuntos 110012 011 e 𝛽 101112 124 são bases do ℝ3 3 Se verdadeiro o item 2 Determine 𝑎 1 2 5𝛼 e 1 2 5𝛽 𝑏 𝐼𝛽 𝛼 e 𝐼𝛼 𝛽 c Verifique que 𝐼𝛽 𝛼 𝐼𝛼 𝛽 1 justifique sua resposta Part II EFT AND HOLISTIC THEORY Holistic Leadership and EFT Combined EFT is ever better when used with an authentic holistic model to keep it clear which part of a person to treat at any moment The Holistic Leadership teachings and model provide just the right holistic context in which to place EFT individually or in groups EFT the Emotional Freedom Technique is a wonderful technique for changing beliefs emotions and unconscious body stresses Although it alone addresses the energy body see the section Energy above EFT is most helpful when combined with an authentic holistic understanding EFT practitioners and trainers often forget the complexity of the 24 energy systems inside the human body and their relationship to the whole They also address energy as indistinctly as mainstream psychology addresses mental mind ie without realizing the distinct types of energy how to deal with them differently or what is the unwelcome consequence of ignoring the difference between them Therefore EFT works best in the context of a holistic modelwith clear guidelines in recognizing the bodys energetic systemswhich discloses the healing targets more precisely Holistic Leadership provides that framework and knowledge Within the Holistic Leadership framework EFT is understood as one useful tool among many to resolve blocks or reduce the pain of inner conflicts EFT precisely works on very specific energy systems to resolve limiting emotions and beliefs so we can advance in the spiritual life EFT when combined with the Holistic Leadership model gives a double perspective in the treatment to distinguish with fine granularity which type of energy and which aspects of the whole must be addressed EFT works inside the inner conflicts that come from the deepest layers in the personalitythe inner child the teenager the ego and even inside the higher self The EFT tapping points are on the meridians mostly inside the physical body but EFT also affects the chakras the aura the bodys nerves and the twodimensional electromagnetic field of the body local magnetic fields And unlike some other therapies or psychodynamic approaches EFT taps directly on the energy systems themselves to unlock stuck energy and to deliver new signals that improve the overall balance and flow in the bodyenergy systems The power of the energy systems is enormous The energy body is the mode by which the physical body gets information from the spirit the soul the mind the personality and its environment The energy body is the medium of communication and control leading outer functions like the immune system the endocrine system and the nervous system It is the foundation of our health not only mental or physical but psychological health because psychological health means communicating harmoniously with ourselves and our environment in body soul and spirit EFT as a tool for clearing inner conflicts from a holistic point of view shows the whole persons energy field before the meaning of acute illness or chronic dysfunction or AIDS or cancer occurs and it can offer resultsnot by curing diseases but by clearing deeply disturbing conflicts that make one sick In contrast with mere symptom correction though it is necessary to combine the glance at the whole when using EFT and resolving the conflicts and causes to prevent the return of the disease or dysfunction In summary EFT works inside and on the energy body which is the information system of our holistic system As a physical technique tapping on the acupuncture and meridian points it allows access and clearing of information regarding emotional mental and spiritual issues in people EFT dramatically improves synergy and amplification power when combined with inspiring new views of human potential and development for spiritual deepening and personal transformation techniques offered by the Holistic Leadership model EFT is not only a technique but a holistic preparation and integration of the soul and the self