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Consider the matrix Find the numbers and such that the vector belongs to the null space of . =[a] =[b]

Suppose the augmented matrix of a linear system has the following reduced echelon form: Find the numbers and  such that the solution of the system in vector parametric form is   =[a] =[b] =[c] =[d]

The solutions of the system of linear equations

The matrices and  are given below

Read the following passage.   Answer the questions IN ENGLISH.  Copy and paste the questions and write your answers in English in the answer space Mi mejor amigo se llama Armando. Él es mexicano. Este semestre vive en Minneapolis con mi familia porque es un estudiante de intercambio (exchange). A él le gusta mucho jugar al fútbol porque es el deporte más popular de todos los países hispanos. Su equipo favorito es el Real Madrid de España. A Armando no le gusta que Minneapolis no tiene un equipo profesional de fútbol. Es imposible jugar fútbol ahora en el invierno, pero a Armando le gustan nuestros inviernos porque puede esquiar en la nieve. También le interesa aprender a jugar al fútbol americano.  Armando es trabajador y simpático. Él tiene cuatro clases de ciencias y un laboratorio de química este semestre. Sus clases son difíciles pero interesantes. Le gustan sus profesoras porque son inteligentes y buenas. Él estudia mucho en la biblioteca con sus amigos durante la semana.  Los sábados y domingos por la noche, nuestro pasatiempo favorito es visitar la plaza central de mi ciudad. Siempre salimos a ver partidos en los bares de deportes. La semana próxima van a jugar Real Madrid y Barcelona. Va a ser un partido muy interesante.    Where does Armando live? What doesn’t Armando like about the winters? What’s the name of Minneapolis’ official soccer team? Why does Armando like his professors? What’s happening next week? Did you write your answers in English.  Your answers must be in English to receive any points.    

X-rays have higher energies than visible light. Which of the following statements is true?

A 48-year-old male presents for his annual physical exam. He has not significant PMH and he is not currently on any medications. He consumes 2 cans of beer weekly and does not smoke. His blood pressure is normal during this visit. His primary care physician orders a fasting lipid panel with the following results:   Laboratory Test Patient Result Normal Range Triglyceride 135 mg/dL < 150 mg/dL HDL 36 mg/dL > 40 mg/dL LDL 220 mg/dL < 130 mg/dL   In addition to diet and exercise, what medication should be started in this patient?

A 20-year-old male presents to the primary care office for a routine wellness visit and is without complaints.  The patient states that he feels entirely well, denies recent acute illness, and has no significant PMH.  On physical examination, heart rate is noted to be irregular.  A baseline EKG is obtained.   Based on this rhythm strip (see image below), what is your initial diagnosis?     

A 62-year-old male with a PMH of polycythemia vera presents to the Emergency Department complaining of sudden onset of pain and paresthesia of the left leg which began 1 hour ago.  Physical examination reveals the left lower extremity is cool to the touch and the toes are cyanotic.  The popliteal pulse is absent by palpation and Doppler.  The left femoral pulse is absent by palpation but weakly present by Doppler.  The right upper and lower extremity pulses are 2+/4+ throughout.  Which of the following conditions is the most likely cause of this patient’s symptoms?

A 56-year-old male patient presents to the Primary Care clinic to establish care and states that he has not seen a medical provider in over 25 years.  The patient is currently without complaints.  Routine laboratory studies are ordered, including a comprehensive metabolic panel, CBC, and fasting lipid profile.  The laboratory reports the appearance of white, opaque serum (see image below) when analyzing the patient’s blood, and the physical examination was notable for the presence of multiple xanthomas over the back, proximal extremities, and chest area.  Based on this information, which of the following laboratory results would you expect to find in this patient?