Let A be a matrix with independent rows. A. Show that AAT is invertible. B. Show that if b is any vector in Col(A), then the equation Ax = b has a solution in Row(A) given by xR = AT (AAT )−1 b. (The matrix AT (AAT )−1 is called the pseudoinverse of A, and is usually denoted by A+ . It is a right inverse of A, and coincides with the two-sided inverse A−1 if A is square.) c. The mapping of Col(A) to Row(A) given by xR = AT (AAT )−1 b is an isomorphism

Answers

Answer 1

Answer:

Attached below

Step-by-step explanation:

Given that A is a matrix with independent rows

A) Prove [tex]AA^{T}[/tex] is invertible

rank of A = number of rows of Matrix A

This shows that | A | ≠ 0  ( i.e. A has a full rank )

also  [tex]|A^{T} |[/tex] ≠ 0

and [tex]|AA^{T}|[/tex] = | A | [tex]|A^{T} |[/tex]   ≠ 0

Hence we can conclude that [tex]AA^{T}[/tex] is invertible

B) Prove that b is any vector in Col( A )

Attached below is the detailed solution

C) Mapping of Col ( A ) to Row ( A )

b is a non-zero vector hence AXr = 0 ( i.e. there is no solution )

also the kernel of the mapping will be Null

show that mapping preserves the operation

attached below is the detailed solution

Let A Be A Matrix With Independent Rows. A. Show That AAT Is Invertible. B. Show That If B Is Any Vector

Related Questions

Please help!! Also please show how to do problem!

Answers

Answer:

118000 thousand cents. Jdbduxb

I'll give brainliest​

Answers

Answer:

7 oof

Step-by-step explanation:

The train journey between London King's cross and Durham is 2hours and 50 minutes. If a train leaves London at 08:40 at what time doses it arrive in Durham?

Answers

Answer:

11:30

Step-by-step explanation:

8:40 + 2 hours = 10:40

10:40 + 20 min = 11:00

11:00 + 30 min = 11:30

help asap, with good explaination please

Answers

Answer:

60 cubes

Step-by-step explanation:

10 times 6

6 are in each layer but there are 12 going down layer by layer

so 10 times 6 equal 60

the actuall answer is 60

= 60

Complete the equation so it will have no solution. 5x - 8 = _ +2

Answers

Answer:

5x

Step-by-step explanation:

If the blank were to be occupied with 5x there would be no solutions

Observe...

5x - 8 = 5x + 2

* subtract 5x from each side *

5x - 5x cancels out

5x - 5x cancels out

we're left with -8 = 2

which is not true

Hence if the blank = 5x the equation will have no solution

Write the equation of the circle with a radius 7 and center (13, 15).


HELP ASAP!!!

Answers

Answer:

Option b is the correct answer

[tex] (x - 13)^2 + (y - 15)^2 = 49 [/tex]

Step-by-step explanation:

[tex] (x - 13)^2 + (y - 15)^2 = 7^2 [/tex]

[tex] (x - 13)^2 + (y - 15)^2 = 49 [/tex]

For each sentence, drag a word that will make the statement true.
Words may be used once or more than once.
always returned to choices list.
sometimesalwaysnever
Equilateral triangles are
acute triangles.

Scalene triangles are
acute triangles.

Right triangles are
acute triangles.

Obtuse triangles are
isosceles triangles.

Answers

Answer:

Equilateral triangles are always acute triangles.

Scalene triangles are sometimes acute triangles.

Right triangles are never acute triangles.

Obtuse triangles are sometimes isosceles triangles.

Step-by-step explanation:

Equilateral triangles are always acute because each angle is 60⁰.

Scalene triangles have sides that are different lengths. They can be right, obtuse, or acute.

A right triangle is never acute because it has a 90⁰ angle. Acute means all angles are less than 90⁰.

An obtuse triangle can be either scalene or isosceles. It always has one angle greater than 90⁰ (obtuse).

Which angle measure is the measure of a straight angle? 100° 0° 90° 180°

Answers

Answer:

180° degrees is a straight angle

Step-by-step explanation:

Answer:

180 degrees

Step-by-step explanation:

A full circle is 360 degrees

A half circle is a straight angle

a straight angle is 180 degrees

938.120 in word form please

Answers

Answer:

nine hundred thirty-eight one hundred twenty thousandths

Step-by-step explanation:

Urgent Need Help! worth 100 points

Answers

the answer to your question is 4 times 6, 4 times 3 + 4 times 3

have a nice day

Answer:

the answer to this math question is

4 times 6, 4 times 3 + 4 times 3

Step-by-step explanation:

Aleks Verfied

What is the longest line segment that can be drawn in a right rectangular prism that is 12 cm long, 11 cm wide, and 8 cm tall?

Answers

When I put the right answer it says it’s wrong

Answer:

The answer is 18.1






John finished his 5 chores in 45 minutes. If he spent the same amount of time on each
chore, how long, in minutes, did it take him to finish each chore?

Answers

Answer:

9 Minutes

Step-by-step explanation:

5x9=45

Brainliest?

9 minutes 5x9=45…………..

Help asap please I really need it!

Answers

Answer:

[tex]volume = \frac{4}{3} \pi r^3\\\\Radius = 2 , volume = \frac{32\pi }{3}cm^3 \\\\Radius = 3, volume = 36\pi cm^3 \\\\Radius = 4, volume = \frac{256\pi }{3} cm^3\\\\Radius= 6, volume = 288\pi cm^3[/tex]

A child swallowed a substance with an LD50 of 6 mg/kg of body weight. It is crucial that the child's stomach be pumped promptly as the material is highly poisonous.


False

True

Answers

Yes, It is crucial that the child's stomach be pumped promptly as the material is highly poisonous.

How to LD50 represents?

The LD50 is a Lethal dose and 50 represents 50 percent of the test animal's population, that is it will be lethal to half of the tested animals. The amount of a toxic agent (such as a poison, virus, or radiation) that is powered to wipe 50 percent of a population of animals on which it is tested.

Therefore, It is crucial that the child's stomach be pumped promptly as the material is highly poisonous.

Learn more about LD50 here: https://brainly.com/question/10042271

#SPJ2

What is the volume, in cubic m, of a cube with an edge length of 11m?
A rectangular prism has a length of 17m, a height of 18m, and a width of 17m. What is its volume, in cubic m?

Answers

11x11x11=1331 m^3
For the Q
17x18x17=5202 m^3
For the rectangular prism

Which equation has a constant of proportionality equal to 10? Choose 1 answer: Choose 1 answer:

Answers

it’s B! I hope I get brainlist!! I hope you have a good day bye!

What is the distance between the following points?
y
5
3
2
1+
++
-9-8-7 -6 -5 -4 -3 -2
-24
-3
-4+
.

Answers

I don’t know I’m just typing so I can get a Anwser for mine

Answer: c. √65

Step-by-step explanation:

that’s what’s right on khan

PLEASE HELP ME ASAP!!! No links please and please give a step by step explanation

Is 547 a term in the sequence 1,8,15,22,29?

Answers

Answer:

no

Step-by-step explanation:

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

Find the area of the circle in terms of Pi. (TT)
10 cm
A

Answers

Answer:

A≈314.16

Step-by-step explanation:

The manager of a snack bar buys bottled water in packs of 35 and candy bars in packs of 20. Then, she sells the items individually. Yesterday, she bought the same number of water bottles as candy bars to sell at the snack bar. If she bought the lowest number of items possible, how many packs of each item did she buy?

Answers

[tex]\Huge\bf{\underline{\red \dag { Aиѕωєя }}} \red \dag[/tex]

4 Packs of water and 7 Packs of candy bars.

So, we wanna know the smallest number that both 35 and 20 will go into.

Find the Least Common Multiple (LCM), but to find the LCM we need to find the prime factorization of each of the following number :-

[tex] \sf {35 = 5(7)}[/tex]

[tex] \sf \red {20 = 5(4)}[/tex]

[tex] \sf {4 = 2(2)}[/tex]

[tex] \sf \red {20 = 5(2)(2)[/tex]

~Now multiply all the numbers by 5 :-

[tex] \sf \pink{5(7)(2)(2) = 35(2)(2) = 70(2) = 140}[/tex]

This means she needs 140 bottles of water and 140 candybars.

Water is sold in packs of 35, this means that she needs :

[tex] \sf \orange{ \frac{140}{35} = 4\: packs \: of \: water}[/tex]

Candy bars are sold in packs of 20, this means she needs :

[tex] \sf \green{ \frac{140}{20} = 7 \: packs \: of \: candy \: bars}[/tex]

_________________________

Martin's bank account balance is negative. Each week that his
account remains negative the bank charges $36.50. Martin did
not make any deposits and now his bank account balance is
-$182.50. How many weeks was his account negative?

Answers

Answer:

5

Step-by-step explanation:

182.50/36.50 per week= 5 weeks

Simplify -2.3f + 0.8f - 16 - 3

Answers

Answer:

− 1.5 f  −19

that's the correct answer.

45 yd
24 yd
What is the length of the hypotenuse?

Answers

Answer= 51
I plugged it into a calculator good luck

Answer:

51

Step-by-step explanation:

A^2+b^2=c^2

That's the formula

could you help me by chance?

Answers

Answer:

27.5

This is because you plug the numbers into the equation. Hope this helps!

Which shows how to determine the volume of the pyramid?

Answers

Answer:

d would be correct

Step-by-step explanation:

A pyramid is a polyhedron formed by connecting a polygonal base and an a a p e x. The basic formula for pyramid volume is the same as for a cone: volume = (1/3) times  base area times height, where height is the height from the base to the a p e x. That formula is working for any type of base polygon and oblique and right pyramids.

what is the 12th term of the sequence: 48,44,40,36...

Answers

Answer:

12

Step-by-step explanation:

The sequence starts at 48, and goes down 4 with each term. That means that we just need to subtract 4 from 48 12 times.

Hope that this helps!

1. The Community Wading Pool is in the shape of a circle. If the radius of the pool is 28 feet, what is the distance around the pool? I need help

Answers

28 feet x 3 == 28373

Answer:

28 feet

Step-by-step explanation:

thank you the same as the guy above me

please help like waaa everywhere it comes up that its impossible

Answers

Answer:

Step-by-step explanation:

If we subtract 7 from both sides, we get -2 on the right.  This is not possible, since absolute values are always 0 or greater.

Find the area of the figure.
14 m
5 m
16 m

Answers

Answer:

Step-by-step explanation:

Seperate the shape into two. 16x2=32cm². 12x11=132cm²

So altogether it would = 164cm²

Please help me with this math problem

Answers

Answer:

80.6 m

Step-by-step explanation:

Coordinates of the points P and Q are (0, 0) and (40, 70) respectively.

Length of the shortcut can be found by using distance formula between two points P and Q.

Length of the shortcut

[tex] = \sqrt{ {(40 - 0)}^{2} + {(70 - 0)}^{2} } \\ \\ = \sqrt{ {40}^{2} + {70}^{2} } \\ \\ = \sqrt{1600 + 4900} \\ \\ = \sqrt{6500} \\ \\ = 80.6225775 \\ \\ \approx \: 80.6 \: m[/tex]

Other Questions
PLEASE HELP I NEED THEM TODAYYYY I WILL GIVE BRAINLYEST Some students were asked to pick their favourite Action Hero.3/5 chose Batman, 20% chose Hulk and the rest chose Iron Man..Write the ratio of Batman: Hulk: Iron Man in Simplest form.Select one:a. 6:2:2b. 60: 20:20 c. 3:1:1 What is one of the worlds oldest animated story techniques? *O Disney moviescave drawingsshadow puppetry Find the measure of the indicated angle. Rearrange the words to be correct: RTAORC LE EDECSP Denver, Engle and Fido are all dogs who eat differing amounts of dog food. Denver gets 8 19 of the dog food. Engle and Fido share the rest of the food in the ratio 2 : 1 What is Fido's share of the dog food? Show your answer as a percentage, rounded to the nearest percent if necessary. How are the high islands of the Pacific formed?A.by connected coral reefs called atollsB.by lagoonsC.by moving glaciersD.by underwater volcanoesPlease select the best answer from the choices providedABCD how did the kansas nebraska act divide the north and south On Monday, a dental hygienist cleans teeth of 5 patients by the time she takes her lunch break at noon. On average, she is able to clean the teeth of 9 patients in 4 hoursWrite a function to represent the number of patients she sees, y, and the number of hours, 2. the hygienist works after lunch on Monday.Enter your answer in the boxPLEASE HELP! Please help ASAP!!! THANKS! When a doctor is able to determine the sex of the fetus during an ultrasound, which stage of development is the fetus in? third trimester blastocyst formation first trimester second trimester What is the main purpose for using active reading strategies?.To learn new and difficult vocabularyB.To develop stronger writing skillsOC.To boost test and quiz scoresODTo interact with a text for greater understanding Question 20Choose whether the following sentence would be written inthe preterite or imperfect tense.When she was a little girl, she used to write poetry.ImperfectPreterite The box plots show data about the number of years that farmworkers have been employed at each of two farms. Which statement is best supported by the information in the box plots? Anna graphs y=4/5x+5 as shown. Select the statements that identify errors,if any,on Annas graph Explain the economic problem that occurs when highly paid and unionized manufacturing jobs are replaced by low paying service jobs such as food service and hotel hospitality services. to what topic can you relate teenage poverty to ? I needs your helps please :) ty When instructed to find the length of HJ in righttriangle HJG, Alex wrote the equationHJHJsin 28 = while Marlene wrote cos 622020Are both students' equations correct? Explainwhy.H+2028OG The valences of metal x,y and z are 1,2 and 3 respectively. What are the formulae of their;a) hydroxides, b) sulphates, c) hydrogen, d) carbonates, e) nitrates, f) phosphates