hus, D satisfying ​(ABC)DequalsI exists. Why does the expression for D found above also satisfy ​D(ABC)equalsI​, thereby showing that ABC is​ invertible? Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice. A. After substituting the expression for​ D, the product DABC simplifies to I by repeated application of the associative property and the definition of inverse matrices. B. After substituting the expression for​ D, left multiplying the product by nothing results in the equation IequalsABCD. C. After substituting the expression for​ D, taking the inverse of both sides of the equation results in the equation IequalsABCD. D. After substituting the expression for​ D, right multiplying the pr

Answers

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

First Question

Option A is correct

Second  Question

Option C is correct

Third   Question

     [tex]D = A^{-1} * B^{-1} * C^{-1}[/tex]

Fourth   Question

  So substituting for D in  (ABC) D =  I

                 [tex](ABC) * A^{-1} * B^{-1} * C^{-1} = I[/tex]

                 [tex]I = I[/tex]

This proof that  ABC is invertible

Step-by-step explanation:

From the question we are told that

   A , B and  C are invertible which means that [tex]A^{-1} , B^{-1}, C^{-1}[/tex] exist

Now

 From the question

          (ABC) D =  I

Where I is an identity matrix

   Now when we multiply both sides by  [tex]A^{-1}[/tex]  we have

          [tex]A^{-1} A BCD = A^{-1} * I[/tex]

          [tex]IBCD = A^{-1}[/tex]

Now when we multiply both sides by  [tex]B^{-1}[/tex]  we have  

         [tex]B^{-1 } *I BCD = A^{-1} * B^{-1}[/tex]

         [tex]I CD = A^{-1} * B^{-1}[/tex]

Now when we multiply both sides by  [tex]C^{-1}[/tex]  we have  

          [tex]C^{-1} * I CD = A^{-1} * B^{-1} * C^{-1}[/tex]

              [tex]I D = A^{-1} * B^{-1} * C^{-1}[/tex]

                 [tex]D = A^{-1} * B^{-1} * C^{-1}[/tex]

So substituting for D in the above equation

                 [tex](ABC) * A^{-1} * B^{-1} * C^{-1} = I[/tex]

                 [tex]I = I[/tex]

This proof that  ABC is invertible

 

Hus, D Satisfying (ABC)DequalsI Exists. Why Does The Expression For D Found Above Also Satisfy D(ABC)equalsI,

Related Questions

Which are the center and radius of the circle with equation (x + 5)2 + (y − 4)2 = 9?
A. (−5, −4); r = 3
B. (5, −4); r = 9
C. (−5, 4); r = 3
D. (5, 4); r = 9

Answers

Answer:

C)

Step-by-step explanation:

*Look at the picture*

Instructions : integrate the following

Answers

You can simplify the integrand:

[tex]\dfrac{3x^2+4x+1}{2x}=\dfrac{3x}2+2+\dfrac1{2x}[/tex]

Then integrate term-by-term:

[tex]\displaystyle\int\frac{3x^2+4x+1}{2x}\,\mathrm dx=\frac32\int x\,\mathrm dx+2\int\mathrm dx+\frac12\int\frac{\mathrm dx}x[/tex]

[tex]=\dfrac{3x^2}4+2x+\dfrac12\ln|x|+C[/tex]

Enter the solution (x, y) to the system of equations shown. y=2x+1 3y=4x+7

Answers

Answer:

Step-by-step explanation:

3(2x + 1) = 4x + 7

6x + 3 = 4x + 7

2x = 4

x = 2

y = 2(2) + 1

y = 4 + 1

y = 5

(2,5)

Answer:

2,5

Step-by-step explanation:

How do you make a decimal into a fraction?

Answers

Answer:

Step 1: Write down the decimal divided by 1, like this: decimal 1.

Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

Step 3: Simplify (or reduce) the fraction.

I really need help with this

Answers

Answer:

A  (-4, 1)B  (2, 5)

Step-by-step explanation:

The current endpoints are ...

  V = (-9, 2)

  W = (-3, 6)

Put each of these in the translation formula to see where the image points are.

  (x, y) ⇒ (x+5, y-1)

  (-9, 2) ⇒ (-9+5), 2-1) = (-4, 1) . . . . point V ⇒ V'

  (-3, 6) ⇒ (-3+5, 6-1) = (2, 5) . . . . . point W ⇒ W'

The new end points are (-4, 1) and (2, 5), matching choices A and B.

Calculate CDEFtrapezium

Answers

。☆✼★ ━━━━━━━━━━━━━━  ☾  

You need to find the length of A F and BC first

Lets call BC --> 'x'

Lets form an equation

9 + 9 + x + x = 28

18 + 2x = 28

- 18

2x = 10

/ 2

x = 5

So now we have the length BC

We can subtract this length from the 11cm to find the vertical height of the trapezium

11 - 5 = 6

Now we have all we need to work it out.

area = (a + b) / 2 x h

area = (5 + 9) / 2 x 6

area = 42 cm^2

Have A Nice Day ❤    

Stay Brainly! ヅ    

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Answer:

42 cm²

Step-by-step explanation:

We can see this shape is made of 2 shapes that we are familiar with which are a rectangle and a trapezium.

⇒ The first step in working out the area of the trapezium is working out the length of CB and then working out the height of trapezium. We are given that the perimeter of the rectangle is 28 cm and we know that opposite sides of a rectangle are equal so we will call the length we want to work out x

→ x + x + 9 + 9 = 28

⇒ Simplify

→ 2x + 18 = 28

⇒ Minus 18 from both sides to isolate 2x

→ 2x = 10

⇒ Divide both sides by 5 to isolate x

→ x = 5

5 cm is the length of CB, we will need to minus that from 11 to find the height of the trapezium so,

11 - 5 = 6. The height of the trapezium is 6

Now we have the height of the trapezium (6), we have the base (9) and we have the top length (5). All we do now is substitute these numbers into the trapezium formula which is

→ 0.5 × ( a + b ) × h

Where 'a' and 'b' are the parallel sides and 'h' is the height

Now we begin to substitute in the values,

→ 0.5 × ( a + b ) × h

⇒ Substitute in the values

→ 0.5 × ( 5 + 9 ) × 6

⇒ Simplify

→ 0.5 × ( 14 ) × 6

⇒ Simplify further

→ 42

The area of the trapezium is 42 cm²

16x^4-25 Which pattern can we use to factor the expression?

Answers

Step-by-step explanation:

Hope this helps you... Lemme know if you don't understand

Of the 34 cars in the parking lot, 12 are blue, 8 are red, 4are white, and 10 are silver. In simplest form, what are the odds in favor that the next car that leaves the lot will be red or white

Answers

Answer:

0.3529411765

Step-by-step explanation:

add red and white and divide it by the total

what is 8 - 3x > -25 because i have been wondering all day

Answers

Answer:

[tex]8 - 3x > -25 : \left[\begin{array}{ccc}solution: x < 11\\Interval Notation:(-\infty,11)\end{array}\right][/tex]

Step-by-step explanation:

[tex]8-3x>-25[/tex]

Subtract [tex]8[/tex] from both sides:

[tex]8-3x-8>-25-8[/tex]

Simplify:

[tex]-3x>-33[/tex]

Multiply both sides by [tex]-1[/tex] (reverse the inequality):

[tex]\left(-3x\right)\left(-1\right)<\left(-33\right)\left(-1\right)[/tex]

Simplify:

[tex]3x<33[/tex]

Divide both sides by [tex]3[/tex] :

[tex]\frac{3x}{3}<\frac{33}{3}[/tex]

Simplify:

[tex]x < 11[/tex]

Hope I helped. If so, may I get brainliest and a thanks?

Thank you, have a good day! =)

What’s the correct answer for this?

Answers

Answer:

D = 23.4 units

Step-by-step explanation:

In the attached file

division concepts
how many times can 9 go into .7632 ?

Answers

Answer:

None! .7632 is smaller than 9.

Step-by-step explanation:

None, did you mean how many times does .7632 go into 9? For that you can just divide 9 by the other number...

Which expression is equivalent to (3b + 2r)+(4b + r)

Answers

Answer:

7 b + 3 r

Step-by-step explanation:

Which statement is true regarding the graphed functions? On a coordinate plane, a straight red line with a positive slope, labeled g of x, crosses the x-axis at (negative 6, 0) and the y-axis at (0, 6). A straight blue line with a negative slope, labeled f of x, crosses the x-axis at (negative 0.75, 0) and the y-axis at (0, negative 2). f(4) = g(4) f(4) = g(–2) f(2) = g(–2) f(–2) = g(–2)

Answers

Answer:

  none of the above

Step-by-step explanation:

The attached graph shows that none of f(-2), f(2), or f(4) matches any of g(-2) or g(4).

None of the offered statements is true.

___

Please report this problem to your teacher.

Answer:

The answer is not C

Step-by-step explanation:

I think the answer is D sooooo Pray it will be

UPDATE IT IS D

HOPE THIS HELP STAY SAFE

Use substitution to solve each system of equations:

x=y+6
x+y=10

Answers

= (y+6) +y =10
= 2y + 6 = 10
= 2y = 4
Y= 2

(60 POINTS) The figure is transformed as shown in the diagram. Describe the transformation.

A) dilation, then reflection

B) reflection, then rotation

C) rotation, then translation

D) translation, then reflection

Answers

Answer:

The solution is rotation, then translation. The figure has been rotated about the origin by 90° and then translated 6 units to the right.

An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation

2000007 350 represents the situation, where t is the number of years the money has been invested. About how long has the

money been invested? Use a calculator and round your answer to the nearest whole number

5 years

7 years

19 years

22 years

Answers

Answer:

  7 years

Step-by-step explanation:

We expect your equation is ...

  200e^(.08t) = 350

Dividing by 200 and taking the natural log, we have ...

  0.08t = ln(1.75)

  t = ln(1.75)/.08 ≈ 7.0

The money has been invested 7 years.

What’s the range of 39, 41, 5, 43, 26, 7, 43, 24, 41

Answers

Answer:

38

Step-by-step explanation:

Range= highest number - lowest number

Range= 43-5

=38

Step-by-step explanation:

Step 1:  Find the highest number and the lowest number

Highest Number → 43

Lowest Number → 5

Step 2:  Find the range by subtract the lowest number from the highest number

Highest Number - Lowest Number

43 - 5

38

Answer:  The range is 38

I need help!!! And fast!!!!

Answers

There are six p's, and those six p's have a total sum of thirty six


6p=36

Divide both sides by six to get the value of p

36/6 is 6

p is equal to six

Which geometric series converges?
CO
Σ(-3) 2-1
Η =1
O
Σ5-1) 2-1
CO
Ο Σ4(-02 - 1
H=1
CO
Σ06(-2) 2-1
h=1

Answers

Answer:

its C

Step-by-step explanation:

i just did it on edge and plus its really not cool to post answers when you dont actually know the answer bc people that actually want to help cant bc there only two answers allowed per question. so please dont answer if your not trying to help.  

The geometric series [tex]\sum_{n=1}^{\infty} 5(-1)^{n-1}[/tex] converges to zero.

What is convergent and divergent geometric series?

A mathematical term denoting an endless series of the form

a + ar + ar² + ar³ + ⋯, where r is referred to as the common ratio. The geometric series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, is a straightforward example.

A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit.

In contrast, a divergent series is one whose partial sums do not reach a limit. The Divergent series usually approaches infinity.

From the given options let us try with [tex]\sum_{n=1}^{\infty} 5(-1)^{n-1}[/tex].

[tex]= 5\sum_{n=1}^{\infty} (-1)^{n-1}.[/tex]

[tex]= 5\sum_{n=1}^{\infty} (-1)^{n}.\frac{1}{-1}[/tex].

[tex]= -5\sum_{n=1}^{\infty} (-1)^{n}.[/tex]

= - 5[- 1 + 1 - 1 + 1 ...+ 1].

= - 5[0].

= 0.

learn more about geometric sequences here :

https://brainly.com/question/19235539

#SPJ7

What is the length of Line segment A C? Round to the nearest tenth.

Answers

Answer:

wheres the info

Step-by-step explanation:

Answer:

A: 10.5 m

Step-by-step explanation:

i think it's A, i may be wrong! hope this helps!!~

write an equation in point-slope form for the line that has a slope of 15 and contains the point (2,−9).

Answers

Answer:

  y +9 = 15(x -2)

Step-by-step explanation:

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . for slope m and point (h, k)

Here, you are given m=15 and (h, k) = (2, -9). Putting these values into the form gives the equation ...

  y +9 = 15(x -2)

the circumference of a circle is 107.81 yards. Find the diameter of the circle to the nearest tenth

Answers

Answer:

68

Step-by-step explanation:

Divide the circumference by pi, approximately 3.14, to calculate the diameter of the circle. For example, if the circumference equals 56.52 inches, divide 56.52 by 3.14 to get a diameter of 18 inches. Multiply the radius by 2 to find the diameter.

Answer:

the answer is attached to the picture

Which are equations? CHECK all that apply.

X+3=12

Z/7+1

25-q

6g=18

2/3m

P/3.5=2.25

9=100-f

K divided by 5.8

Answers

Answer:

X + 3 = 12

6g = 18

P/3.5 = 2.25

9 = 100 - f

Step-by-step explanation:

Equations have equal signs.

Expressions do not.

Therefore, any expression with an equal sign is an equation, making it one of the correct answers.

Answer:

X + 3 = 12

6g = 18

P/3.5 = 2.25

9 = 100 - f

Step-by-step explanation:

Just did  it!

list down all the prime numbers which are factors of 30

Answers

Hey!!

Here's your answer:

prime numbers which are factors of 30 are:

1,2,3 and 5

Hope it helps

Answer:

1, 2, 3, 5

sorry for the confusion i didn't read it correctly

plzzzzzzzz i need help

Michael is cutting a 100-yard ribbon into pieces 3.4 yards long. He says that an inequality that represents his project is 3.4x < 100. Explain what this statement means, in words, and what each part of the inequality represents.

Answers

Answer:

Okay well the 3.4 yard pieces are the constant in which Michael will be cuttings that number stays the same an will not change. The (X) represents the unknown number of how many times the ribbon will be cut. As the whole inequality states the unknown number of pieces that are 3.4 yards long are less than 100 yards.

Answer:

The variable, x, is the number of pieces of ribbon Michael cuts. Since each piece is 3.4 yards long, 3.4x is the total length of all the pieces together. This total length cannot be more than the 100 yards of ribbon he has, so 3.4x must be less than or equal to 100.

Carl earned grades of 62, 78, 59, and 89 on four math tests.
What is the mean of his grades?
A. 68.5
B. 70
C. 72
D. 74
E. 75.5

Answers

Answer:

Mean, m = 72

Step-by-step explanation:

It is given that, Carl earned grades of 62, 78, 59, and 89 on four math tests.

It is required to find the mean of his grades.

Mean of a data is given by :

[tex]m=\dfrac{\text{sum of observations}}{\text{total no of observations}}[/tex]

Sum of observations is 62 + 78 + 59 + 89 = 288

Total no of observations are 4

So, mean of his grades is :

[tex]m=\dfrac{288}{4}\\\\m=72[/tex]

So, the mean of his grades is 72.

Option C is correct. If Carl earned grades of 62, 78, 59, and 89 on four math tests, the mean of his grades is 72

Mean is the average of the given data. It is expressed mathematically as:

[tex]\overlibe x=\frac{\sum x}{N}[/tex]

[tex]\sum x[/tex] is the sum of the variables

N is the total test taken

[tex]\sum x = 62 + 78 + 59 + 89\\\sum x = 288\\\\N = 4[/tex]

Substitute the resulting values into the mean formula:

[tex]\overline x = \frac{288}{4}\\ \overline x =72[/tex]

This shows that the mean of his grades is 72

Learn more here:https://brainly.in/question/2401311

3y + 6 = 18y

- What does the ( y ) variable stand for and how exactly do you find it?

Answers

Answer:

y=2/5 or 0.4

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

3y + 6 = 18y -->

subtract 3y from both sides to get rid of it.

6 = 15y -->

isolate the variable by dividing it by 15.

6/15 = 15y/15 -->

simplify.

2/5 = y

ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.

Answers

Answer:

  B.  5x^2 -4

Step-by-step explanation:

(f+g)(x) = f(x) + g(x)

  = (4x^2 +1) +(x^2 -5) . . . . . . substitute for f(x) and g(x)

  = x^2(4 +1) +(1 -5) . . . . . . . . collect terms

(f+g)(x) = 5x^2 -4

Find the real solution(s) of the equation. Round your answer to two decimal places when appropriate. 5x^6=30

Answers

Answer:

The real solutions are

[tex]x=\sqrt[6]{6}\approx 1.35\\\\\:x=-\sqrt[6]{6}\approx -1.35[/tex]

Step-by-step explanation:

The solution, or root, of an equation is any value or set of values that can be substituted into the equation to make it a true statement.

To find the real solutions of the equation [tex]5x^6=30[/tex]:

[tex]\mathrm{Divide\:both\:sides\:by\:}5\\\\\frac{5x^6}{5}=\frac{30}{5}\\\\\mathrm{Simplify}\\\\x^6=6\\\\\mathrm{For\:}x^n=f\left(a\right)\mathrm{,\:n\:is\:even,\:the\:solutions\:are\:}x=\sqrt[n]{f\left(a\right)},\:-\sqrt[n]{f\left(a\right)}\\\\x=\sqrt[6]{6}\approx 1.35\\\\\:x=-\sqrt[6]{6}\approx -1.35[/tex]

helpp me nowwwwwww dew Help Marshmello i wasn't born yesterday. xd

Answers

Answer: A) DE = 24 yd and EF = 10 yd

Step-by-step explanation:

Shape EFD is just a dilate of 2, meaning BCA x 2.

13 x 2 = 26

12 x 2 = 24

5 x 2 = 10

Therefore, DE = 24 yd and EF = 10 yd

I hope this helps!

Answer:

DE = 24, EF = 10

Step-by-step explanation:

We can use ratios to solve

13 ft           12 ft

---------- = -----------

26 ft          x ft

Using cross products

13x = 12*26

Divide each side by 13

13x/13 = 12*26/13

x = 24

13 ft           5 ft

---------- = -----------

26 ft          y ft

Using cross products

13y = 5*26

Divide each side by 13

13y/13 = 5*26/13

y = 10

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