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determine whether the linear transformation T is invertible by considering its matrix

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole ISBN: 9780538735452 298

Solution for problem 6.6.21 Chapter 6

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition | ISBN: 9780538735452 | Authors: David Poole

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Problem 6.6.21

determine whether the linear transformation T is invertible by considering its matrix with respect to the standard bases. If T is invertible, use Theorem 6.28 and the method of Example 6.82 to find T 3

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Lecture Notes March 9 , 2016 Reproduction and Development  Anatomy and Physiology o Gametogenesis- the production of gametes  Spermatogenesis- production of sperm- in the testes located in a sack like structure called the scrotum- occurs continuously throughout a male’s reproductive life  Testes have two functional components o Seminiferous tubules- where the sperm is produced o Interstitial Cells- secrete the male sex hormone- testosterone  During spermatogenesis the cells lining the seminiferous tubules are called 1° spermatocytes (2N)  2° spermatocytes (N)  become spermatids ----differentiation (lose cytoplasm and grow tail) Sperm (Spermatozoa)  Sperm have little food reserve and die within 72 hours, but in very low temperatures they can survive for years  Men must release 100 million sperm during intercourse to be considered fertile- some men release 1 billion per ejaculation  Oogenesis- production of eggs in the ovaries- suspended in the abdominal cavity  Two functions of ovaries o Produce the oocytes o Secrete female sex hormones- estrogen and progesterone  Begins before the female is born o Oogonia 1° oocytes (2N) (born with 3-400K) 2° oocytes o Happens once a month only one created  During cytokinesis one of the two cells formed during meiosis gets less cytoplasm- polar body 1  Secondary oocytes are in a sack structure called the follicle  At puberty ovaries begin to release one 2° oocyte every 28 days- ovulation  Ovulation begins when a follicle near the surface of the ovary begins to grow and fill with fluid  Eventually the pressure inside the follicle becomes so great that it ruptures and the 2° oocyte is released into the abdominal cavity  Meiosis II only occurs if the 2° oocyte is penetrated by a sperm  During Meiosis II another polar body is formed- three of the four eggs disintegrate  Once the true egg is formed- fertilization can take place and the zygote 2N is formed Lecture Notes  Since the female has been carrying 1° oocyte for many years the chances that mutations have occurred is much higher than for male sperm o Of the 3-400K oocytes only 13 are ovulated each year o Not very many are released throughout a females life and they will all disintegrate around the age of 50 o Male Reproductive Tract  A coiled tube called the epididymis lies on the surface of the testes and carries the sperm to the vasteferens  That’s what gets cut when you have a vasectomy  Vasteferens (2) run into the abdominal cavity and join the urethra just beyond the point where it leaves the bladder  The urethra passes through the penis and empties to the outside  As the sperm passes through the vasterferens and the urethra seminal fluids added to form semen (seminal fluid + sperm = semen)  Seminal fluid is produced by three glands o Seminal vesicles o Prostate o Cowper’s  Seminal Fluid has four main functions o Vehicle for the transport of sperm o Lubrication of passages o Chemical buffer against the acids in the female reproductive tract o Contains sugars- provide sugars which provide energy to the sperm o Female Reproductive Tract  From the ovary 2° oocyte travels through the abdominal cavity and is swept into the oviduct/ fallopian tube  The swept down the fallopian tube into the uterus  Uterus- pair shaped and muscular  If 2° oocyte is entered by a sperm meiosis II occurs, egg is fertilized and implants on uterine wall  If egg is not penetrated it passes through the cervix into the vagina during menstruation

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Chapter 6, Problem 6.6.21 is Solved
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Textbook: Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign)
Edition: 3
Author: David Poole
ISBN: 9780538735452

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determine whether the linear transformation T is invertible by considering its matrix