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In Exercises 5–8, write a matrix equation that determines

Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald ISBN: 9780321982384 49

Solution for problem 7E Chapter 1.10

Linear Algebra and Its Applications | 5th Edition

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Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald

Linear Algebra and Its Applications | 5th Edition

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Problem 7E

Problem 7E

In Exercises 5–8, write a matrix equation that determines the loop currents. [M] If MATLAB or another matrix program is available, solve the system for the loop currents.

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Female Reproductive System Study Guide: • Why is the reproductive role of females more complex ◦ because of pregnancy • What is the functions of ovaries or female gonands ◦ produce female gonads (ovum) ◦ secretes female sex hormones,estrogen and progesterone • Where is the internal genitalia located ◦ pelvic cavity • What does the internal genitalia include ◦ ovaries and duct system (uterine tubes,uterus,and vagina) • What are external genitalia ◦ external sex organs • What are the two poorly defined regions of the ovaries ◦ outer cortex- houses forming gametes ◦ inner medulla- contains large blood vessels and nerves • How is each ovary held in place ◦ by serval ligaments ◦ ovarian ligaments= anchors medially to uterus ◦ suspensory ligaments= anchors ovary laterally to pelvic wall ◦ mesovarium= suspends ovary;encloses and hods ovaries in place • What are the suspensory ligament and mesovarium apart of ◦ broad ligament= supports uterine tubes,uterus,and vagina • What are ovarian follicles ◦ immature egg (oocyte) +surrounding cells (follicle cells or granulose cells) • What is the process of oogenesis ◦ eggs production ◦ In fetus:oogonia stem cells divide through mitosis and become primary oocytes ◦ start meiosis but arrested in late prophase 1 until puberty ◦ after puberty primary oocyte finish meiosis 1--> first polar body (haploid) and secondary oocyte ◦ secondary oocyte begins meiosis 2 but arrested at metaphase 2 and is ovulated ◦ if no sperm penetrates= oocyte deteriorates ◦ if sperm penetrates= secondary oocytes finishes meiosis 2-->second polar body and ovum • What are the four different types of follicles in follicular development ◦ Primordial Follicle= primary oocyte +single layer of follicle cells ◦ Primary Follicle= primary oocyte + single layer of enlarged follicle cells ◦ Secondary follicle= primary oocyte + multiple layers of granulosa cells ◦ Vesicular (astral) follicle= with larger killed antrum (cavity);secondary oocyte sitting on stalk of cells • What is ovulation ◦ process where a single,secondary oocyte ejected from ovary into fallopian tube;occurs once a month • What is the corpus luteum in follicular development ◦ "yellow body" ruptured follicle after ovulation ◦ secrete progesterone and estrogen to maintain pregnancy until placenta takes over • What is the corpus albicans in follicular development ◦ "white body" ◦ if no pregnancy;scar left after corpus lateen regresses • What is the steps in follicular development ◦ primal follicle-->primary follicle-->secondary follicle-->vesticular follicle-->ovulation-->corpus lutuem-->corpus albicans • What are the differences between the male and female reproductive system ◦ oogenesis vs.spermatogenesis ◦ menstrual cycle= only 1 oocyte related each month compared to 20-150 million sperm ejaculation ◦ women are born with all the gametes they will ever have,unlike male who have continuous production of gametes ◦ product of oogenesis= 1 gamete and for men= 4 viable gametes ◦ spermatogenesis starts at puberty where as oogenesis starts in fetus • What are the uterine tubes ◦ receive ovulated oocyte ◦ site of fertilization • How long are the uterine tubes ◦ 4 inches • What are the three structures of the uterine tubes ◦ ampulla= enlarged distal ends of tube where fertilization takes place ◦ infundibulum= funnel-shaped end of tube with ciliated projections (timbre) that drape over ovary ◦ isthmus= constricted proximal region where ureteric tube joins uterus • What are the uterine tubes composed of ◦ sheets of smooth muscle that move oocyte towards uterus ◦ highly folded mucosa with ciliated cells and non ciliated cells (secrete moist,nutritive fluid) • What is the uterus ◦ hollow ,muscular organ that receives,retains,and nourishes a fertilized ovum ◦ anterior to rectum and superior to bladder ◦ 3 inches long • What are the three regions of the uterus ◦ body,fundus,cervix • What are the three layers of the uterine wall ◦ perimetrium- serous layer ◦ myometrium= smooth muscle expels baby during childbirth ◦ endometrium= mucosal lining where embryo implants,sheds if no implantation occurs • What is the vagina ◦ thin walled tube extending from cervix to body exterior ◦ 3-4 inches long ◦ organ of copulation- chamber for sperm deposition • What are the three layers of vaginal wall ◦ adventitia,muscular,mucosa (contains rugae) • What are the five parts to the female external genitalia ◦ Mon Pubis= rounded fatty area overlaying pubic symphysis ◦ Labia ‣ Labia majora= lateral skin folds:homologous to scrotum ‣ Labia Minora= medial skin folds:homologous to ventral penis ◦ Vestibule= recess enclosed by labia minor that contains external urethral and vaginal orifices ◦ Greater vestibular glands= mucous secreting glands on posters-lateral sides of vaginal opening for lubrication:homologous to bulbourethral glands ◦ Clitoris= partially protruding structure composed of erectile tissue (corpora cavernosa);anterior to urethral office;homologous to glans penis • What is the function of mammary glands ◦ produce milk to nourish newborns ◦ modified sweat glands (technically part of the integumentary system) • What is the anatomy of the mammary glands ◦ Areola= ring of pigmented skin ◦ Nipple= protrusion in center of areola that contains openings to lactiferous ducts ◦ Lobules= contain glandular alveoli with secretory cells and myoepithelial cells that produces milk ◦ Lactiferous ducts= carry milk to lactiferous sinuses that open to outside of nipple ◦ suspensory ligaments= attach great to underlying muscle • What is Oogenesis ◦ production of female gametes takes years to complete • How does Oogonia multiply ◦ by mitosis and it store nutrients • Where are primary oocytes developed ◦ in primordial follicles that become surrounded by follicle cells ◦ begin meiosis but stall in prophase I • What happens each month to primary oocytes ◦ a few primary oocytes are activated ◦ one from this group is selected each month to become a dominant follicle that resumes meiosis I • After Meiosis I is completed,what happens to the primary oocytes ◦ two haploid cells of different sizes are produced ◦ Secondary oocyte- large cell with almost all the mothers cytoplasm and organelles ◦ first polar body- almost devoid of cytoplasm • What happens to the secondary oocyte after its arrest in metaphase II ◦ becomes the ovulated ovum,if not penetrated by sperm it deteriorates ◦ if penetrated by sperm,second oocyte completes second meiosis yielding,ovum and second polar body • What are the differences between Oogenesis and Spermatogenesis ◦ Number of functional gametes differ ‣ Oogenesis= produces one viable ovum with three polar bodies;unequal division ensure oocyte has ample nutrients for 6-7 day journey to uterus • polar bodies degenerate and die ‣ Spermatogenesis= produces for viable sperm ◦ Error rate differs ‣ spermatogenesis has an error rate of 3-4% ‣ Oogenesis has an error rate of 20% • What is the function of the uterus ◦ Hollow,thick walled muscular organ that receives,retains,and nourishes fertilized ovum • What is the position of the uterus ◦ Anteverted= inclined forward (normal position) ◦ Retroverted= inclined backwards • What are the regions of the uterus ◦ Body-major portion ◦ Fundus- rounded superior region ◦ Isthmus- narrowed inferior region ◦ Cervix- narrow neck,or outlet;projections into vagina ◦ Cervical Canal- communicates with the vagina via external os and uterine body via internal os • What do cervical glands do ◦ secrete mucus that blocks sperm entry except during mid cycle • What is cervical cancer ◦ affects 450,000 women worldwide,killing half ◦ Pap smear for detection ◦ Gardisil Shots in three doses helps prevent it ◦ frequent inflammation of cervix,STIs,multiple pregnancies are risks • What four structure help support the uterus ◦ mesometrium= lateral support of broad ligament ◦ Cardinal (lateral cervical) ligament= from cervix and superior vagina to pelvic lateral walls ◦ Uterosacral ligaments= secure uterus to anterior wall ◦ Round Ligaments= binds uterus to anterior wall • Are mammary gland present in both males and females ◦ yes,but usually only functional in females • What is the main function of mammy glands ◦ production of milk to nourish newborns • How many modified sweat glands are in the mammary glands ◦ 15-25 lobes • What is the most common malignancy and second most common cause of cancer death in the U.S. women ◦ Breast Cancer • Where does breast cancer usually arise from ◦ arises from epithelial cells of smallest ducts that eventually metabolize • What are some risk factors of breast cancer ◦ early onset menstruation and late menopause ◦ no pregnancies or first pregnancy late in life ◦ no or short periods of breast feeding ◦ family history of breast cancer ◦ 70% of women with breast cancer have no known risk factor • What is 10% of the cause of breast cancer ◦ hereditary defects including mutations to genes BRCA1 and BRCA2;50-80% of women with these genes develop breast cancer ◦ great risk of ovarian cancer as well • What is the ovarian cycle ◦ monthly series of events associated with the maturation of an egg • What are the two phases of the ovarian cycle ◦ Follicular phase- period of vesicular follicle growth;days 1-14 ◦ Luteal Phase- period of corpus luteum activity;days 14-28 ◦ ovulation occurs mid cycle between phases ◦ only 10-15% of women have 28-day cycles ◦ luteal phase is always 14 days from ovulation to end of cycle • What is the process of follicular development ◦ A primal follicle becomes a primary follicle (squamous like cells become cuboidal) ◦ Primary Follicle becomes secondary follicle (form stratified epithelium;granulose cells) ◦ Secondary follicle becomes vesicular follicle (theca folliculi,zona pelluccida,antrum) • During follicular phase,several vesicular (astral) follicles are stimulated to grow.What is this triggered by ◦ rising levels of FSH • When FSH levels drop in the middle of follicular phase what happens ◦ cause only one antral follicle,dominant follicle,to continue on • During Ovulation,what do rising levels of LH cause ◦ ovary wall rupture,expelling secondary oocyte with its corona radiata to peritoneal cavity • What is Mittelschmerz ◦ twinge of pain sometimes felt at ovulation by some women • How are fraternal twins produced ◦ 1-2% of ovulations release more than one secondary oocyte,which if fertilized results in fraternal twins • How are identical twins produced ◦ result from fertilization of one oocyte,then separation of daughter cells • What is referred to as corpus hemorrhagicum in the luteal phase of ovarian cycle ◦ after ovulation,ruptured follicle collapses,and antrum fills with clotted blood • What happens to the remaining granulose and thecal cells ◦ they enlarge and form the corpus luteum which secretes some progesterone and estrogen • What happens in the luteal phase if no pregnancy occurs ◦ corpus luteum degenerates into corpus albicans in 10 days • What happens if pregnancy occurs ◦ corpus leteum produces hormones that sustain pregnancy until placenta takes over at about 3 months • What is your Uterine menstrual cycle ◦ monthly changes in uterine environment • What is the menstrual phase of the uterine cycle ◦ uterus sheds all but the deepest part of the endometrium,estrogen/progesterone;day 1-5 • What is the proliferative phase of the uterine cycle ◦ rising levels of estrogen cause endometrium to rebuild itself and cervical mucus thins to allow sperm to pass into uterus;days 6-14 • What day does ovulation occur ◦ day 14 • What is the secretory phase of the uterine cycle ◦ rising levels of progesterone increases vascularization of endometrium,prepares it for implantation of embryo,endometrial glands enlarge,cervial mucus thickens,enlarge and secrete glycogen into uterus to nourish embryo until implantation is complete • Why does the cervical mucus thicken in the secretory phase of the uterine cycle ◦ forms plug to block sperm/pathogens from entering uterus • What are the major hormones involved in the regulation of cycles ◦ Gonadotropin-releasing hormone (GnRH)- stimulates anterior pituitary to release follicle stimulating hormone (FSH) and lutenizing hormone (LH) ◦ FSH- stimulates follicle growth ◦ LH- stimulates follicle maturation,stimulates thecal cells to produce androgens and causes ovulation ◦ Estrogen- sex hormone,analogous to testosterone ‣ promote oogenesis and follicle growth ‣ induce secondary sexual characteristics (breasts) ‣ promotes endometrial growth during proliferative phase of uterine cycle ◦ progesterone= sex hormone,promotes secretory phase of menstrual cycle • What is an ectopic pregnancy ◦ oocyte fertilized in peritoneal cavity/distal portion of tube develops there • What is Pelvic inflammatory disease ◦ due to an infection in peritoneal cavity ◦ can cause scarring of the uterine tubes/ovaries • What is a babies sex genetically determined by ◦ XY= male ◦ XX=female ◦ 44 autosomes +2 sex chromosomes • What initiates development of the male reproductive structures ◦ SRY gene on theY chromosome • What is the anatomy of a 5-6 week old fetus ◦ gonadal ridge- future gonads ◦ Mullarian ducts- further female ducts;fallopian tubes;uterus;cervix;upper 1/3 of vagina ◦ Wolffian ducts- future male ducts;epididymis;ductus deferens;and the seminal vesicles ◦ GenitalTubercle- small projection on external surface;gives rise to external genitalia ◦ Labioscrotal swelling= swelling inferolateral to genital tubercle • What week does development for a male begin and what happens during that period ◦ week 7 ◦ Mullarian ducts regresses,testes form from gonadal ridge ◦ Seminiferous tubules form in gonadal ridges and joinWolffian ducts via efferent ductules ◦ Wolffian duct develops • When does the external genitalia from for a male ◦ week 8 ◦ penis from from genital tubercle ◦ labioscrotal swellings form the scrotum • When do testes descend from abdominal cavity into scrotum ◦ 2 months before birth • When does female reproductive development begin and what happens there ◦ week 8 ◦ wolffian duct regresses ◦ ovaries form from gonadal region ◦ Mullerian ducts develop • What happens when a female's external genitalia starts to develop ◦ clitoris forms from genital tubule ◦ labioscortal swelling becomes the labia majora • What is fertilization ◦ sperm's chromosome combine with chromosomes of secondary oocytes forming a zygote (the initial cell) • When are the sperm and oocyte viable for fertilization ◦ sperm= 24-48 hours after ejaculation ◦ oocyte= 12-24 hours post ovulation • How many days per month is a women fertile ◦ 3 days • What is the fate of sperm during fertilization ◦ 1.leak out of vagina ◦ 2. Destroyed by acidic environment in vagina ◦ 3.blocked at cervix ◦ 4.phagocytes destroys them ◦ 5.reverse peristalsis guides sperm to oocyte and secretions in female repro.tract capacitate sperm ‣ sperm motility enhanced ‣ membranes become thin so that enzymes can be released from acrosome (organelle around head of sperm,contains enzymes) • What is the process of fertilization ◦ 1.sperm releases enzymes that digest junctions between granulose cells surrounding oocyte ◦ 2.sperm binds to zona pellucida ◦ 3.acrosomal reaction- sperm relate acrosomal enzymes that digest holes through the zone pellucida ◦ 4.one sperm binds and fuses to the plasma membrane of oocyte ◦ 5.cytoplasmic contents of sperm enter oocyte ◦ 6.oocyte completes meiosis II ◦ 7.cortical reaction prevents polyspermy (enzymes released by oocyte destroy its sperm receptors and zone pellucid hardens) ◦ 8.The 2 nuclei fuse forming the zygote • What is pregnancy ◦ events that occur from fertilization until infant is born • What is the gestation period ◦ length of time women is pregnant;280 days • What is the embryonic period ◦ fertilization to week 8 • What is the fetal period ◦ week 9 to birth • What is the cleavage period ◦ rapid miotic divisions • What is the cleavage process ◦ 36-hours:1st cleavage creates 2 identical cells called blastomeres ◦ 72 hours- morula (16 or more cells) ◦ 4-5 days- blastocyst: ‣ cluster of 100 cells,fluid filled cavity,zone pellucida breaks down ‣ Trophoblast= single layer of large flattened cells;aids in implantation,role in placenta formation,protect embryo from mother's immune system ‣ Inner cell mass= internal cluster of 20-30 cells;forms embryo and 3 extra embryonic membranes ◦ 6-7 days:implantation of blastocyst into endometrium begins • What is Human Chronic gonadotropin ◦ at implantation a hormone is released from trophoblast,stimulates corpus luteum to keep secreting estrogen and progesterone • What happens at post-implantation ◦ chorion develops from trophoblast,takes over stimulating corpus luteum • What are the four extra embryonic membranes ◦ Amnion= develops from inner cell mass of blastocyst;transparent membranous sac that fills with amniotic fluid for protection and temperature regulation ◦ Yolk sac= develops from the inner cell mass of blastocyst and provides some nutrients to developing embryo ◦ Allantois= form as out pocket from end of yolk sac,its blood vessels become part of the umbilical cord,becomes part of urinary bladder ◦ Chorion= develops from trophoblast and develops chorionic vili that form part of placenta • What is gastrulation ◦ formation of 3 primary germ layers • What are the three primary germ layers ◦ ectoderm= becomes epidermis,hair,skin,nails,skin glands,brain and spinal cord ◦ endoderm= becomes epithelial linings of digestive,respiratory,urogenital systems and associated glands ◦ mesoderm= becomes everything else • What are some developmental milestones ◦ between 2-3 months= placenta fully formed and functional ◦ 5 weeks= brain,spinal cord,other organs developing,heart begins beating ◦ 8 weeks- arms,legs face developing ◦ 9-12 weeks= head dominant,retina of eye forms,genital sex evident,hematopoiesis begins ◦ 13-16 weeks= eyes and ears developing ◦ 17-20 weeks= can feel fetal movement ◦ 21-30= substantial weight gain and fetus visible at 24 weeks ◦ 31-40 weeks= slowed weight gain,subcutaneous fat being deposited • What is parturition ◦ birth/labor- fetus expelling from uterus • What is the process of labor ◦ initiation= rise in estrogen triggers formation of oxytocin receptors in cells of myometrium; estrogen causes braxton hicks contractions ‣ Fetus begin producing oxytocin: • stimulate placenta to release prostaglandins • oxytocin and prostaglandins stimulate rhythmic contractions of myometrium • + feedback loop:mother's hypothalamus triggers relate of oxytocin from posterior pituitary,more prostaglandin released from placenta-->greater myometrium contraction ◦ Dilation stage= cervix dilates to 10 cm and effaces or thins ◦ Expulsion stage= strong uterine contractions use baby out ◦ Placental stage= uterus continues contracting to expel placenta and attached fetal membranes • What is lactation ◦ production of milk by mammary glands ◦ mammary glands develop during pregnancy • What is colostrum ◦ "first milk"- immunoglobins (antibodies),antimicrobial proteins (lactoferrin),and antibacterials (lysozyme) • What is the composition of true milk ◦ fat.protein,sugar,provide energy ◦ minerals,vitamins hormones,water,immunofactors,bacteria • What are prolactin and oxytocin ◦ prolactin-stimulates milk production ◦ oxytocin= causes milk let-down reflex

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Textbook: Linear Algebra and Its Applications
Edition: 5
Author: David C. Lay; Steven R. Lay; Judi J. McDonald
ISBN: 9780321982384

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In Exercises 5–8, write a matrix equation that determines