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
qaws [65]
3 years ago
5

If A is nonsingular, then (AT )-1 =(A-1) T . (a) Verify this theorem for 2 × 2 matrices

Mathematics
1 answer:
kipiarov [429]3 years ago
3 0

Answer:

Verified

Step-by-step explanation:

Let the 2x2 matrix A be in the form of:

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

Where det(A) = ad - bc # 0 so A is nonsingular:

Then the transposed version of A is

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

Then the inverted version of transposed A is

(A^T)^{-1} = \frac{1}{ad - cb} \left[\begin{array}{cc}a&-c\\-b&d\end{array}\right]

The inverted version of A is:

A^{-1} = \frac{1}{ad - bc}\left[\begin{array}{cc}a&-b\\-c&d\end{array}\right]

The transposed version of inverted A is:

(A^{-1})^T = \frac{1}{ad - bc}\left[\begin{array}{cc}a&-c\\-b&d\end{array}\right]

We can see that

(A^T)^{-1} = (A^{-1})^T

So this theorem is true for 2 x 2 matrices

You might be interested in
If 8% of all cell phones are defective, and you have a random sample group of 100 Samsung Galaxy Vills,
Sati [7]

Answer:

Mean = 8

Variance = 7.36

Standard Deviation = 2.7129

Step-by-step explanation:

This is a binomial distribution with parameters, n and p.

Where

n is sample size (given as 100)

p is the probability of success, or probability of defective (given as 8% or 0.08)

The mean, variance, standard deviation formula for binomial distribution is shown below:

Mean = np

Variance = npq

Standard Deviation = \sqrt{npq}

Where q would be probability of failure, or "1 - p"

Thus,

n = 100

p = 0.08

q = 1 - 0.08 = 0.92

SO, we have:

Mean = np=100*0.08=8

Variance = npq=100*0.08*0.92 = 7.36

Standard Deviation = \sqrt{npq}=\sqrt{7.36}=2.7129

5 0
3 years ago
What is the solution set -4.9x +1.3 > 11.1
Irina18 [472]

Answer:

x < - 2

Step-by-step explanation:

given - 4.9x + 1.3 > 11.1 ( subtract 1.3 from both sides )

- 4.9x > 9.8 ( divide both sides by - 4.9 )

Remembering to reverse the direction of the inequality symbol as a result of dividing by a negative quantity.

x < - 2 ← inequality reversed

solution set : x ∈ ( - ∞, - 2 )


8 0
2 years ago
Simplify the linear expression
vekshin1

Answer:

\huge\boxed{-\frac{7}{8}a - \frac{1}{6}}

Step-by-step explanation:

This question utilizes combining like terms and common denominators. First you have to convert both terms including "a" to have a denominator of 8. You would do this by multiplying both the numerator, and the denominator by the same value. This value in the case of -\frac{1}{4} a would be 2, and in the case of \frac{2}{3} the value would be 2. This would result in the equation: -\frac{5}{8}a+\frac{4}{6}-\frac{2}{8}a-\frac{5}{6}. Then simply combine like terms to get your final answer.

5 0
2 years ago
16x 2 + 8x - 15 Mathematics?
Gala2k [10]
If you're factoring, your answer is

(4x - 3)(4x + 5)

You'll work it out this way:

16x^2 + 8x - 15

Since there's no GCF here, you multiply the first and third terms, giving you -240. Your next step is to find two numbers that have a sum of 8 and a product of -240. These numbers are 20 and -12. Plug those in and you've got:

16x^2 + 20x - 12x - 15

From here you divide it into two binomials. These are (16x^2 + 20x) and (-12x - 15).
When you take out the greatest common factors (4x and -3), they become:

4x(4x + 5) - 3(4x + 5)

Then you group what's outside of the parentheses together (4x - 3)
And bring what's inside of the parentheses down (4x + 5).
This brings your answer to

(4x - 3)(4x + 5)
5 0
3 years ago
Which unit would you most likely use to represent the time it takes to drive to your friend's house, which is five miles from yo
Leokris [45]

Answer:

C. minutes

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Other questions:
  • Which function transforms the graph of y=x^2 so that it is first shifted down 4 units and is then reflected across the y-axis?
    11·1 answer
  • What is the explicite to 19,13,7,1,...
    7·1 answer
  • According to chebyshev's theorem, at least what percent of the observations lie within plus and minus 1.75 standard deviations o
    5·1 answer
  • Geometry help?????????????????????
    11·1 answer
  • To synthesize information regarding when books were written, Alex should create a
    6·2 answers
  • Richard bought a car for $2,500. The value of the car depreciates by 5% each year,
    5·2 answers
  • Mai skated miles, and Clare skated 3/5 farther than that. Write an expression for the distance Clare
    9·2 answers
  • What is the answer? 10 + (–4) =
    12·2 answers
  • You are about to list your house as For Sale By Owner. Suppose you need to allow
    7·1 answer
  • Function g can be thought of as a translated (shifted) version of f(x) = x2.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!