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scZoUnD [109]
3 years ago
12

Some basic properties of eigenvalues. Show the following: a) The eigenvalues of A and AT are the same. b) A is invertible if and

only if A does not have a zero eigenvalue. c) If the eigenvalues of A are λ1, . . . , λn and A is invertible, then the eigenvalues of A−1 are 1/λ1, . . . , 1/λn. d) The eigenvalues of A and T −1AT are the same. Hint: you’ll need to use the facts that det A = det(AT), det(AB) = det A det B, and, if A is invertible, det A−1 = 1/ det A.
Mathematics
1 answer:
Nitella [24]3 years ago
5 0

Answer:

Step-by-step explanation:

a) Since for any determinant we have

|A|=|A^T|

|A- lemda I  |=0 then |A^T-lemda I |=0

Hence both determinants would have the same eigen values

b) If A is having a zero value then by definition of eigen values we get

|A|=0. Hence we say if A is invertible if and only if A does not have a zero eigen value

c) |AA^{-1}|=1\\

|A^{-1} |=\frac{1}{|A|}

Hence eigen values of A would be the reciprocals of that of A transpose.

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Round 80531 to the nearest thousand.
Iteru [2.4K]
That would be 8,1000
6 0
3 years ago
Read 2 more answers
Sylvia has a piece of material that is 668.36 square inches. She marked the material into 4 equal pieces and then cut out one of
sveta [45]

The whole magic jug had 668.36 ounces of mysterious elixir in it.
Sylvia came along and marked it into 4 equal amounts, so each
amount was  (1/4)  of  (668.36 ounces).

Now, you would have us believe, she tucked the magic jug under her cloak,
walked quickly and quietly down the hall into the shadows, pulled the jug out,
and quaffed one of the equal amounts from it, all in one slug.

The quantity remaining in the jug was then 

                     (3/4) of (668.36 ounces)  =  501.27 ounces.

The same process works for length, volume, area, stones, money, anything.
If you divide up what you have into 4 equal parts, then each part is 1/4 .
If you eat, sell, lose, or give away  1/4  of it, you have  3/4  left.

8 0
3 years ago
Read 2 more answers
Construction paper cost $0.10 per square inch. How much will Susan spend to make this figure out of construction paper? ​
AfilCa [17]

The will spend $33.60 (option C) to make the figure out of construction paper, if the construction paper cost $0.10 per square inch.

Step-by-step explanation:

The given is,

                 Construction paper cost $0.10 per square inch

                 Pyramid diagram with dimensions

Step:1

               Formula to calculate the area of pyramid,

                            Area, A = lw+l\sqrt{(\frac{w}{2}) ^{2} + h^{2} } +w \sqrt {(\frac {l} {2}) ^{2} + h^{2} }..............(1)

             Where,

                        l - Base length

                      w - Base width

                      h - Height of pyramid

             From given,

                       l = 12 inches

                     w = 12 inches

            For height of pyramid,

             By using Pythagorean theorem,

                                       Hypotenuse^{2} = Base^{2} + Height ^{2}.................(2)

              For right angle triangle,

                                             Base = \frac{12}{2} = 6 inches

              Equation (2) becomes,

                                                  8^{2} = 6^{2} + Height^{2}

                                        Height^{2} = 8^{2} - 6^{2}

                                        Height^{2} = 64 -36 = 28

                                          Height = \sqrt{28}

                                          Height = 5.2915 inches

                    h - 5.2915 inches

                Equation (1) becomes,

                       A = (12)(12)+(12)\sqrt{(\frac{12}{2}) ^{2} + 5.2915^{2} } +(12 )\sqrt {(\frac {12} {2}) ^{2} + 5.2915^{2} }

                          = 144+(12)\sqrt{(36+27.999)} +(12)\sqrt{(36 + 27.999)}    

                          = 144+(12)\sqrt{63.999}+(12)\sqrt{63.999}

                          = 144+(12)(7.9999)+(12)(7.9999)

                          =144+95.999+95.999

                          =335.998      

                          ≅ 336 square inches

                Where,

                         $0.10 per square inch ( from given)

                 Paper cost of total figure = 336 square inches

                                                             = 336 × 0.10

                                                             = $ 33.60

Result:

           The will spend $33.60 to make the figure out of construction paper, if the construction paper cost $0.10 per square inch.

8 0
3 years ago
Write a problem situation to match the inequality: x divided by 4 less than or equal to 5
Paha777 [63]

Answer:

yes it is ill explain

Step-by-step explanation:Find the student's error in solving the following inequality.31 < -5x + 625 < -5x-5 < x

The student should have added 6 to both sides instead of subtracting it.

The student divided 25/-5 incorrectly.

The student should have switched the direction of the inequality sign to get -5> x for a final answer.

The student should have switched the direction of the inequality sign to get -5> x for a final answer.

Find the student's error in solving the following inequality.2 < -3x -4 < 56 < -3x < 5-2 > x > -5/3

The student should have added 4 to all parts (left, middle, and right) to get 6 < -3x < 9.

The student divided 6/-3 incorrectly.

The student should not have switched the direction of the sign in the final step.

The student should have added 4 to all parts (left, middle, and right) to get 6 < -3x < 9.

Which answer choice is a solution to the inequality ?

-1

1

1.5

0

1.5

Identify the property used in each step of solving the inequality .

Step 2: Addition property

Step 3: Multiplication property

Which numbers are solutions to the inequality 2x - 1 > x + 2? Check all of the boxes that apply.

4, 5

If x < 5 and x > c, give a value of c such that there are no solutions to the compound inequality. Explain why there are no solutions

Sample response: The value of c could be 5 or any number greater than 5.

The solution is the intersection of both solution sets of the given inequalities.

The solutions of the compound inequality must be solutions of both inequalities.

A number cannot be both less than 5 and greater than 5 at the same time.

Identify the graph of the inequality 2(2x - 1) + 7 < 13 or -2x + 5 -10.

C

Briyana has $150, and she needs to save at least $560 for a spring break trip. If she can save $45 per week, how long will it take her to save enough money?Let w = weeks saving money. Write an inequality to describe the situation.

45w + 150 560

What is the fewest number of full weeks Briyana would have to work to have enough money?

10 weeks

Three times two less than a number is greater than or equal to five times the number. Find all of the numbers that satisfy the given conditions.Let n = a number. Choose the inequality that represents the given relationship.

3(n - 2) Greater than symbol5n

Which of the following is the solution set of the problem?

(-infinite symbol , -3]

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8 0
3 years ago
Read 2 more answers
Need help asap please! Thanks!
KonstantinChe [14]
The diagram tells us 3 things: the right angle and the two corresponding side measurements. Because the side measurements are corresponding, we can set a proportion:

6/9=9/15

If this proportion is true, it means the triangles are similar. If this proportion is impossible, it means the triangles are no similar.

To calculate this, we use cross multiplication.

6/9=9/15

6*15=9*9
90=81

90 does not equal 81 making this proportion impossible, which concludes that these two triangles are not similar.

I hope this helps! Please comment if you have any questions.
5 0
3 years ago
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