Find the perimeter. Simplify the answer

It looks like given matrices are supposed to be

[tex]\begin{array}{ccccccc}\begin{bmatrix}3&2\\2&3\end{bmatrix} & & \begin{bmatrix}1&-1\\2&-1\end{bmatrix} & & \begin{bmatrix}1&2&3\\0&2&3\\0&0&3\end{bmatrix} & & \begin{bmatrix}3&1&1\\1&3&1\\1&1&3\end{bmatrix}\end{array}[/tex]

You can find the eigenvalues of matrix A by solving for λ in the equation det(A - λI) = 0, where I is the identity matrix. We also have the following facts about eigenvalues:

• tr(A) = trace of A = sum of diagonal entries = sum of eigenvalues

• det(A) = determinant of A = product of eigenvalues

(a) The eigenvalues are λ₁ = 1 and λ₂ = 5, since

[tex]\mathrm{tr}\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3 + 3 = 6[/tex]

[tex]\det\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3^2-2^2 = 5[/tex]

and

λ₁ + λ₂ = 6   ⇒   λ₁ λ₂ = λ₁ (6 - λ₁) = 5

⇒   6 λ₁ - λ₁² = 5

⇒   λ₁² - 6 λ₁ + 5 = 0

⇒   (λ₁ - 5) (λ₁ - 1) = 0

⇒   λ₁ = 5 or λ₁ = 1

To find the corresponding eigenvectors, we solve for the vector v in Av = λv, or equivalently (A - λI) v = 0.

• For λ = 1, we have

[tex]\begin{bmatrix}3-1&2\\2&3-1\end{bmatrix}v = \begin{bmatrix}2&2\\2&2\end{bmatrix}v = 0[/tex]

With v = (v₁, v₂)ᵀ, this equation tells us that

2 v₁ + 2 v₂ = 0

so that if we choose v₁ = -1, then v₂ = 1. So Av = v for the eigenvector v = (-1, 1)ᵀ.

• For λ = 5, we would end up with

[tex]\begin{bmatrix}-2&2\\2&-2\end{bmatrix}v = 0[/tex]

and this tells us

-2 v₁ + 2 v₂ = 0

and it follows that v = (1, 1)ᵀ.

Then the decomposition of A into PDP⁻¹ is obtained with

[tex]P = \begin{bmatrix}-1 & 1 \\ 1 & 1\end{bmatrix}[/tex]

[tex]D = \begin{bmatrix}1 & 0 \\ 0 & 5\end{bmatrix}[/tex]

where the n-th column of P is the eigenvector associated with the eigenvalue in the n-th row/column of D.

(b) Consult part (a) for specific details. You would find that the eigenvalues are i and -i, as in i = √(-1). The corresponding eigenvectors are (1 + i, 2)ᵀ and (1 - i, 2)ᵀ, so that A = PDP⁻¹ if

[tex]P = \begin{bmatrix}1+i & 1-i\\2&2\end{bmatrix}[/tex]

[tex]D = \begin{bmatrix}i&0\\0&i\end{bmatrix}[/tex]

(c) For a 3×3 matrix, I'm not aware of any shortcuts like above, so we proceed as usual:

[tex]\det(A-\lambda I) = \det\begin{bmatrix}1-\lambda & 2 & 3 \\ 0 & 2-\lambda & 3 \\ 0 & 0 & 3-\lambda\end{bmatrix} = 0[/tex]

Since A - λI is upper-triangular, the determinant is exactly the product the entries on the diagonal:

det(A - λI) = (1 - λ) (2 - λ) (3 - λ) = 0

and it follows that the eigenvalues are λ₁ = 1, λ₂ = 2, and λ₃ = 3. Now solve for v = (v₁, v₂, v₃)ᵀ such that (A - λI) v = 0.

• For λ = 1,

[tex]\begin{bmatrix}0&2&3\\0&1&3\\0&0&2\end{bmatrix}v = 0[/tex]

tells us we can freely choose v₁ = 1, while the other components must be v₂ = v₃ = 0. Then v = (1, 0, 0)ᵀ.

• For λ = 2,

[tex]\begin{bmatrix}-1&2&3\\0&0&3\\0&0&1\end{bmatrix}v = 0[/tex]

tells us we need to fix v₃ = 0. Then -v₁ + 2 v₂ = 0, so we can choose, say, v₂ = 1 and v₁ = 2. Then v = (2, 1, 0)ᵀ.

• For λ = 3,

[tex]\begin{bmatrix}-2&2&3\\0&-1&3\\0&0&0\end{bmatrix}v = 0[/tex]

tells us if we choose v₃ = 1, then it follows that v₂ = 3 and v₁ = 9/2. To make things neater, let's scale these components by a factor of 2, so that v = (9, 6, 2)ᵀ.

Then we have A = PDP⁻¹ for

[tex]P = \begin{bmatrix}1&2&9\\0&1&6\\0&0&2\end{bmatrix}[/tex]

[tex]D = \begin{bmatrix}1&0&0\\0&2&0\\0&0&3\end{bmatrix}[/tex]

(d) Consult part (c) for all the details. Or, we can observe that λ₁ = 2 is an eigenvalue, since subtracting 2I from A gives a matrix of only 1s and det(A - 2I) = 0. Then using the eigen-facts,

• tr(A) = 3 + 3 + 3 = 9 = 2 + λ₂ + λ₃   ⇒   λ₂ + λ₃ = 7

• det(A) = 20 = 2 λ₂ λ₃   ⇒   λ₂ λ₃ = 10

and we find λ₂ = 2 and λ₃ = 5.

I'll omit the details for finding the eigenvector associated with λ = 5; I ended up with v = (1, 1, 1)ᵀ.

• For λ = 2,

[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}v = 0[/tex]

tells us that if we fix v₃ = 0, then v₁ + v₂ = 0, so that we can pick v₁ = 1 and v₂ = -1. So v = (1, -1, 0)ᵀ.

• For the repeated eigenvalue λ = 2, we find the generalized eigenvector such that (A - 2I)² v = 0.

[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}^2 v = \begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}v = 0[/tex]

This time we fix v₂ = 0, so that 3 v₁ + 3 v₃ = 0, and we can pick v₁ = 1 and v₃ = -1. So v = (1, 0, -1)ᵀ.

Then A = PDP⁻¹ if

[tex]P = \begin{bmatrix}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 0 & -1\end{bmatrix}[/tex]

[tex]D = \begin{bmatrix}5&0&0\\0&2&0\\0&2&2\end{bmatrix}[/tex]

Answer: First do 145 - 25, which is 120. Then do 120 ÷ 15 = 8. Therefore the slope intercept is y ÷ 15 = x. Their voyage will last 8 days.

Explanation: Brainliest please

Answer: On a coordinate plane, a cube root function goes through (negative 8, negative 2), has an inflection point at (0, 0), and goes thorugh (8, 2).

Step-by-step explanat hope that help

The function is

[tex]\\ \sf\longmapsto f(x)=\sqrt[3]{x}[/tex]

Graph attached

Answer:

30

Step-by-step explanation:

Answer:

Step-by-step explanation:

For every 30 minutes she dances, Nell stretches for 10 minutes

Ratio:

A degree in a polynomial function is the greatest exponent of that equation, which determines the most number of solutions that a function could have and the most number of times a function will cross the x-axis when graphed.

Answer:

x = 6

y = 8

Explanation and graph is given in picture

I hope it helps.

Answer:

44 - 47 is -3 if thats what youre asking

Step-by-step explanation:

Answer: a = 2.5 (an-1)

Step-by-step explanation: trust me;)

The function which is used to represent the geometric progression 8, 20, 50, 125, 312.5, ... is [tex]a_{n} = 8(2.5)^{n-1}[/tex].

sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is as a geometric sequence of  numbers.

[tex]a_{n} =ar^{n-1}[/tex]

Where,

[tex]a_{n}[/tex] is the nth term of the sequence or geometric progression

n is the total number of terms

r is the common ratio

and a is the first term

According to the given question

We have

A geometric progression

8, 20, 50, 125, 312.5

Now the common ratio for the above progression is given by

[tex]r = \frac{20}{8} = 2.5[/tex]

And the first term is

a = 8

Therefore, the function which is used to represent the above sequence is given by

[tex]a_{n} = 8(2.5)^{n-1}[/tex]

Hence, the function which is used to represent the geometric progression 8, 20, 50, 125, 312.5, ... is [tex]a_{n} = 8(2.5)^{n-1}[/tex].

Learn more about geometric progression here:

https://brainly.com/question/4853032

#SPJ2

Answer:

156.73 cm

Step-by-step explanation:

height of the person = (2.75 × humerus length)+71.48 cm

length of the found humerus = 31cm

∴ height of the person = (2.75 × 31)+71.48 cm

                                     = 85.25 + 71.48 cm

                                     = 156.73 cm

Answer:

  (a)  Ginny made a mistake in step 1 when she identified b = 31. It should be b=–31.

Step-by-step explanation:

The value of b is the coefficient of x. In the given quadratic expression, the coefficient of x is -31, so Ginny should have started with b = -31 in step 1.

Answer:

A

Step-by-step explanation:

Answer:

180/7

Step-by-step explanation:

Answer:

(-3,16)

Step-by-step explanation:

(-5,12)

f (x) = ( (x+5) (x+5) ) + 12

f (x) = x^2 + 10x + 37

(-2,15)

f (x) = ( (x+2) (x+2) ) + 15

f (x) = x^2 + 4x + 19

Answer:

3600

Step-by-step explanation:

Answer:

3600

Step-by-step explanation:

verificando :)

Answer:

  5.48 lb

Step-by-step explanation:

12 inches is 1 foot.

12.8 times that length will have 12.8 times that weight:

  12.8 · 0.428 lb = 5.4784 lb ≈ 5.48 lb

__

The given values have 3 significant figures, so the answer needs to be rounded to 3 significant figures.

Answer:

Radius = 3.232 cm to the nearest thousandth.

Step-by-step explanation:

Volume of a sphere = 4/3πr^3, so:

45π = 4/3πr^3     π is common to both sides, so:

45 = 4/3 r^3

r^3 = 45 * 3/4

r^3 = 33.75

r = 3.232 cm.

Step-by-step explanation:

5x+3x-14=180

8x-14=180

8x=180+14

8x=174

x=174/8

x= 21.75°

if x is 21.75°, then 5x is 108.75°

which means 3x-14 is 51.25°

therefore, f +108.75+51.25=180

f = 180-160

f=20°

Answer:

Not sure but I think it's B.

Answer:

for the die it's a 4 to 6 chance and the coin is a 50% chance

Answer:

see explanation

Step-by-step explanation:

(10)

Since the triangles are congruent then corresponding sides are congruent, so

EF = BC , that is

4x - 1 = 19 ( add 1 to both sides )

4x = 20 ( divide both sides by 4 )\

x = 5

and

DE = AB , that is

y - 6 = 8 ( add 6 to both sides )

y = 14

-------------------------------------------------------

(11)

Since the triangles are congruent the corresponding angles are congruent, so

∠ K = ∠ Y , that is

3x - 37 = 41 ( add 37 to both sides )

3x = 78 ( divide both sides by 3 )

x = 26 , then

∠ K = 3x - 37 = 3(26) - 37 = 78 - 37 = 41°

The sum of the 3 angles in Δ ZMK = 180° then

∠ Z = 180° - (41 + 112)° = 180° - 153° = 27°

So

∠ A = ∠ Z

2y + 7 = 27 ( subtract 7 from both sides )

2y = 20 ( divide both sides by 2 )

y = 10

------------------------------------------------------------------------

(12)

Since the triangles are congruent the corresponding sides and angles are congruent

DG = BS

4x - 11 = 25 ( add 11 to both sides )

4x = 36 ( divide both sides by 4 )

x = 9

∠ T = 180° - (56 + 21)° = 180° - 77° = 103°

Then

∠ H = ∠ T

7y + 5 = 103 ( subtract 5 from both sides )

7y = 98 ( divide both sides by 7 )

y = 14

Answer:

I believe its 42.5 or 42500

Step-by-step explanation:

if its not right im so so so so sorry

Answer:

it depends on how much Annika has and if she is willing to give Susan money

Step-by-step explanation:

I could have answered properly but i do not understand the question it just states that, look below

How much money should Annika give Susan?

Step-by-step explanation:

you don't understand what the multiplication or division with 10 (or a higher power of 10) does ?

or you don't know. what 10² means ?

this means 10 to the power of 2 or 10 squared and is simply 10 multiplied with itself 2 times : 10×10.

and 10×10 is ... 100.

as you can imagine, this is not restricted to the number 2 (and 10). "power of" can be any number and just indicates how often the base number is multiplied with itself.

a surcharge case is "power of 0", which is simply 1.

now that we understand that, let's have a quick look at how the numbers we are dealing with (in daily life as well as in class and in science) are actually built :

when I write e.g the number

1234

then this actually means

4×10⁰ + 3×10¹ + 2×10² + 1×10³

when I multiply this now by e.g. 10 this becomes

4×10⁰×10 + 3×10¹×10 + 2×10²×10 + 1×10³×10 =

4×10¹ + 3×10² + 2×10³ + 1×10⁴

as you can see, the previous "single" position 4 now becomes a 40.

and the result looks in short form :

12340

so, a multiplication by 10 adds a 0 at the low end of the number.

a multiplication by 10² or 100 (= 10×10) adds then 2 0s at the low end. and so forth.

a division by 10 does the opposite and removes a 0 at the low end of the number.

but what if we don't have any 0 at this position of the number ? then we enter the system of the decimal point.

because on the right side of the decimal point we continue to countdown the exponent of 10 below 0.

the first position right of the decimal point stands for 10^‐1, the second position for 10^‐2, and so forth. and that is nothing else than tenths, hundredths, thousandths, ...

so, in short, a multiplication by 10 moves the decimal point one position to the right. and if we run out of written positions, then we can simply assume an infinite sequence of 0s continuing further to the right.

and a division by 10 moves the decimal point one position to the left. and if we run out of written positions, then we can simply assume an infinite sequence of 0s continuing further to the left too that are then showing up on the right side of the decimal point.

now, I think we covered all the basics and we can look at the question here :

10² × 18.72

10² = 100 = 10×10

so, we are multiplying twice by 10 and move the decimal point therefore 2 positions to the right.

the result is then

1872

as a little guide : when it is clear that the number has to get bigger by the operation (like a multiplication by 10 or 100), you need to move the decimal point in the direction that makes the number bigger (which is to the right).

and if the operation is clearly trying to make the number smaller, then you have to move the decimal point in the direction to make the number smaller (to the left).

Answer:

Therefore, Aroha is 17 yrs old and her brother is 14 yrs old.

Step-by-step explanation:

Let's represent Aroha's brother's Agee with the letter "b" yrs old.

If Aroha is 3yrs older than her brother, she's : (b+3) yrs old.

The sum of their ages is 31,

b+(b+3)=31

2b+3=31

Collect like terms,

2b=31-3

2b=28

Divide both sides by 2,

b=14

b+3=17

A cheerful teen hoping this helps,

stay techy, brilliant and positive!

Answer:

1. 5⁴

2. d¹⁰

3. w⁶

Answer:

let me think about this

Step-by-step explanation:

question i may help

This is a combination equation:

14C8 = 14!/8!(6!) = 3003

Answer: 3003

Answer: 19,38, and 33.

Step-by-step explanation:

80=2x+x+2x-5=5x=95=x=19

Answer: (7,3)

Step-by-step explanation:

[Please check]:   I decoded the equations as follows:

3x-4y=9 and −5x+4y=-23

We can solve this by either of two methods:  Algebra and graphing.

Algebra:

Add the two equations:

  3x-4y=9

−5x+4y=-23

-2x = -14

   x = 7

Use x=7 to solve for y:

3x-4y=9

3(7)-4y=9

21 -4y = 9

-4y = -12

y = 3

----

The solution is (7,3)

======

Graphing:

See the attached graph.  The lines intersect at (7,3)

Answer:

Faster the deadline is so close let me sing

Super idol di show lung domini ding shaw

Super idol di show lung domini ding shaw

Super idol di show lung domini ding shaw

Answer:

Step-by-step explanation:

6x - 17 = 3x + 7

3x = 24

x = 8