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
OverLord2011 [107]
3 years ago
15

If A is an n× n matrix, then det A = det AT . Verify this theorem for 2 × 2 matrices.

Mathematics
1 answer:
Bond [772]3 years ago
4 0

Answer:

Verified

Step-by-step explanation:

Let A matrix be in the form of

\left[\begin{array}{cc}a&b\\c&d\end{array}\right]

Then det(A) = ad - bc

Matrix A transposed would be in the form of:

\left[\begin{array}{cc}a&c\\b&d\end{array}\right]

Where we can also calculate its determinant:

det(AT) = ad - bc = det(A)

So the determinant of the nxn matrix is the same as its transposed version for 2x2 matrices

You might be interested in
Please Help..........................
jasenka [17]
The exact circumference is 60ft
8 0
3 years ago
Read 2 more answers
The probability of pulling an orange is 2 out of 5 if I 20 times how many of them would be orange
telo118 [61]
The answer would be 8.
4 0
3 years ago
The scores on the GMAT entrance exam at an MBA program in the Central Valley of California are normally distributed with a mean
Kaylis [27]

Answer:

58.32% probability that a randomly selected application will report a GMAT score of less than 600

93.51%  probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600

98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 591, \sigma = 42

What is the probability that a randomly selected application will report a GMAT score of less than 600?

This is the pvalue of Z when X = 600. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{600 - 591}{42}

Z = 0.21

Z = 0.21 has a pvalue of 0.5832

58.32% probability that a randomly selected application will report a GMAT score of less than 600

What is the probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600?

Now we have n = 50, s = \frac{42}{\sqrt{50}} = 5.94

This is the pvalue of Z when X = 600. So

Z = \frac{X - \mu}{s}

Z = \frac{600 - 591}{5.94}

Z = 1.515

Z = 1.515 has a pvalue of 0.9351

93.51%  probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600

What is the probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600?

Now we have n = 50, s = \frac{42}{\sqrt{100}} = 4.2

Z = \frac{X - \mu}{s}

Z = \frac{600 - 591}{4.2}

Z = 2.14

Z = 2.14 has a pvalue of 0.9838

98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600

8 0
3 years ago
Each of the letters of the word ALABAMA are written on a piece of paper and then
Kruka [31]

Answer:

3/7

Step-by-step explanation:

There are 7 letters in ALABAMA. And there are 4 A's in ALABAMA. So if you're trying to not get an A then you would subtract 4 from 7. Which you would get 3/7 of the letters in ALABAMA are not A.

7 0
2 years ago
The probability that a randomly chosen citizen-entity of Cygnus is of pension age† is approximately 0.7. What is the probability
victus00 [196]

Answer: 0.2401

Step-by-step explanation:

The binomial distribution formula is given by :-

P(x)=^nC_xp^x(1-p)^{n-x}

where P(x) is the probability of x successes out of n trials, p is the probability of success on a particular trial.

Given : The probability that a randomly chosen citizen-entity of Cygnus is of pension age† is approximately: p =0.7.

Number of trials  : n= 4

Now, the required probability will be :

P(x=4)=^4C_4(0.7)^4(1-0.7)^{4-4}\\\\=(1)(0.7)^4(1)=0.2401

Thus, the probability that, in a randomly selected sample of four citizen-entities, all of them are of pension age =0.2401

5 0
3 years ago
Other questions:
  • Any help is good but kinda hard
    15·1 answer
  • Evaluate f(x)=6x² – 12 when x=-3.<br> A -30<br> B 42<br> C -48<br> D 312
    9·2 answers
  • Evaluate -8w + 3z when w = 2.2 and z = -9.1.
    13·2 answers
  • Express these fractions and mixed numbers as a percent.
    5·1 answer
  • A rectangle is a four sided flat shape where every integer angle is a right angle. Therefore, opposite sides are parallel and co
    6·1 answer
  • Lynn bought a bag of grapefruit, 1 5/8 pounds of apples, and 2 3/16 pounds of bananas. The total weight of her purchase was 7 1/
    15·1 answer
  • PLEASE HELP URGENT
    6·1 answer
  • Solve for x, check the image below
    13·2 answers
  • 4. Write as a fraction in simplest form: 38 minutes to 12 minutes
    6·1 answer
  • Find an angle with a positive measure and an angle with a negative measure that is coterminal with each angle 210° and - 120°
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!