1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Neporo4naja [7]
3 years ago
12

For this exercise assume that all matrices are ntimesn. Each part of this exercise is an implication of the form​ "If "statement

​ 1", then​ "statement 2"." Mark an implication as True if the truth of​ "statement 2" always follows whenever​ "statement 1" happens to be true. An implication is False if there is an instance in which​ "statement 2" is false but​ "statement 1" is true. Complete parts​ (a) through​ (e). Justify each answer.
a. If there is an ntimesn matrix D such that AD equals​I, then there is also an ntimesn matrix C such that CA equalsI. Choose the correct answer below.
A. False; by the Invertible Matrix Theorem if the equation Ax 0 has only the trivial solution, then the matrix is not invertible Thus, A cannot be row equivalent to the nxn identity matrix
B. True: by the Invertible Matrix Theorem if equation Ax= 0 has only the trivial solution, then the equation matrix is not invertible. Thus, A cannot be row equivalent to the nxn identity matrix. Ax - b has no solutions for each b in R". Thus, A must also be row equivalent to the n x n identity matrix °
C. True; by the Invertible Matrix Theorem if the equation Ax=0 has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the n x n identity matrix.
D. False; by the Invertible Matrix Theorem if the equation Ax 0 has only the trivial solution, then the matrix is not invertible; this means the columns of A do not span R". Thus, A must also be row equivalent to the nx n identity matrix
Mathematics
1 answer:
inna [77]3 years ago
5 0

Answer:

C. True; by the Invertible Matrix Theorem if the equation Ax=0 has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the n x n identity matrix.

Step-by-step explanation:

The Invertible matrix Theorem is a Theorem which gives a list of equivalent conditions for an n X n matrix to have an inverse. For the sake of this question, we would look at only the conditions needed to answer the question.

  • There is an n×n matrix C such that CA=I_n.
  • There is an n×n matrix D such that AD=I_n.
  • The equation Ax=0 has only the trivial solution x=0.
  • A is row-equivalent to the n×n identity matrix I_n.
  • For each column vector b in R^n, the equation Ax=b has a unique solution.
  • The columns of A span R^n.

Therefore the statement:

If there is an n X n matrix D such that AD=​I, then there is also an n X n matrix C such that CA = I is true by the conditions for invertibility of matrix:

  • The equation Ax=0 has only the trivial solution x=0.
  • A is row-equivalent to the n×n identity matrix I_n.

The correct option is C.

You might be interested in
Wright et al. [A-2] used the 1999-2000 National Health and Nutrition Examination Survey(NHANES) to estimate dietary intake of 10
xxMikexx [17]

Complete question :

Wright et al. [A-2] used the 1999-2000 National Health and Nutrition Examination Survey NHANES) to estimate dietary intake of 10 key nutrients. One of those nutrients was calcium in all adults 60 years or older a mean daily calcium intake of 721 mg with a standard deviation of 454. Usin these values for the mean and standard deviation for the U.S. population, find the probability that a randonm sample of size 50 will have a mean: (mg). They found a) Greater than 800 mg b) Less than 700 mg. c) Between 700 and 850 mg.

Answer:

0.10935

0.3718

0.9778

0.606

Step-by-step explanation:

μ = 721 ; σ = 454 ; n = 50

P(x > 800)

Zscore = (x - μ) / σ/sqrt(n)

P(x > 800) = (800 - 721) ÷ 454/sqrt(50)

P(x > 800) = 79 / 64.205295

P(x > 800) = 1.23

P(Z > 1.23) = 0.10935

2.)

Less than 700

P(x < 700) = (700 - 721) ÷ 454/sqrt(50)

P(x < 700) = - 21/ 64.205295

P(x < 700) = - 0.327

P(Z < - 0.327) = 0.3718

Between 700 and 850

P(x < 850) = (850 - 721) ÷ 454/sqrt(50)

P(x < 850) = 129/ 64.205295

P(x < 700) = 2.01

P(Z < 2.01) = 0.9778

P(x < 850) - P(x < 700) =

P(Z < 2.01) - P(Z < - 0.327)

0.9778 - 0.3718

= 0.606

3 0
2 years ago
You are saving to buy a new phone you have $150 in your bank account and can save $55 each week assuming you don’t spend any mon
FromTheMoon [43]

Answer:

150+55w

Step-by-step explanation:

150+55w

150 never changes

(55)(w), 55 changes depending on number of weeks

8 0
3 years ago
Read 2 more answers
John leaves his home. He travels 5 blocks south and three blocks west. As the crow flies, how far is John from his home?
riadik2000 [5.3K]

Answer:

5.83 blocks away from his home

Step-by-step explanation:

If he travels 5 blocks south and 3 blocks west, the distance from his house considered along with the distances travelled gives a right angled triangle whose opposite side and adjacent sides are the distances travelled north and west.

The distance from his house after moving 3 blocks west is the hypotenuse side. As such, the distance may be computed using Pythagoras' theorem. Let the distance from his house be G

G^2 = 5^2 + 3^2

G^2 = 25 + 9

= 34

G = √34

=5.83

John is 5.83 blocks away from his home

3 0
3 years ago
Is this positive, negative, none or you cannot tell. Will mark CORRECT brainliest
pshichka [43]

Answer:

Positive correlation if right. Atleast consider brainlist:)

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
C = 188.4in <br> What’s the answer
Advocard [28]

Answer:

Well from where the equation is now, I don't see any further things I can do. What is the context of the problem?

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Is a scalene triangle a regular polygon
    5·1 answer
  • If you are asked to create a box plot about data that has two different sets, do would you make 1 or 2 box plots?
    14·1 answer
  • REALLY NEED HELP<br> What is the quotient of 3227/555? What is the repetend
    12·1 answer
  • PLEASE can someone explain why The exact value of sec ( π/6) is 2 /√ 3 ??
    8·1 answer
  • Jeremy says that if you translate, rotate, or reflect a polygon, the area of the image is the same as the area of the original f
    13·1 answer
  • Solve the inequality 1+5(x-8)&lt;2-(x+5)
    14·2 answers
  • Use integers to represent the values in the statement.
    7·1 answer
  • SWEET POINTS IF YOI TELL ME WHAT THIS IS !!
    10·1 answer
  • What are/is the coefficient(s): 47 &gt; 7m - 9
    7·1 answer
  • Please help !! Find the value of x
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!