find the spectral radius of A. Is this a convergent matrix? Justify your answer. Find the limit x=lim x^(k) of vector iteration
Answers
Answer:
The solution to this question can be defined as follows:
Step-by-step explanation:
Please find the complete question in the attached file.
[tex]A = \left[\begin{array}{ccc} \frac{3}{4}& \frac{1}{4}& \frac{1}{2}\\ 0 & \frac{1}{2}& 0\\ -\frac{1}{4}& -\frac{1}{4} & 0\end{array}\right][/tex]
now for given values:
[tex]\left[\begin{array}{ccc} \frac{3}{4} - \lambda & \frac{1}{4}& \frac{1}{2}\\ 0 & \frac{1}{2} - \lambda & 0\\ -\frac{1}{4}& -\frac{1}{4} & 0 -\lambda \end{array}\right]=0 \\\\[/tex]
[tex]\to (\frac{3}{4} - \lambda ) [-\lambda (\frac{1}{2} - \lambda ) -0] - 0 - \frac{1}{4}[0- \frac{1}{2} (\frac{1}{2} - \lambda )] =0 \\\\\to (\frac{3}{4} - \lambda ) [(\frac{\lambda}{2} + \lambda^2 )] - \frac{1}{4}[\frac{\lambda}{2} - \frac{1}{4}] =0 \\\\\to (\frac{3}{8}\lambda + \frac{3}{4} \lambda^2 - \frac{\lambda^2}{2} - \lambda^3 - \frac{\lambda}{8} + \frac{1}{16}=0 \\\\\to (\lambda - \frac{1}{2}) (\lambda -\frac{1}{4}) (\lambda - \frac{1}{2}) =0\\\\[/tex]
[tex]\to \lambda_1=\lambda_2 =\frac{1}{2}\\\\\to \lambda_3 = \frac{1}{4} \\\\\to A = max {|\lambda_1| , |\lambda_2|, |\lambda_3|}\\\\[/tex]
[tex]= max{\frac{1}{2}, \frac{1}{2}, \frac{1}{4}}\\\\= \frac{1}{2}\\\\(A) =\frac{1}{2}[/tex]
In point b:
Its
spectral radius is less than 1 hence matrix is convergent.
In point c:
[tex]\to c^{(k+1)} = A x^{k}+C \\\\\to x(0) = \left(\begin{array}{c}3&1&2\end{array}\right) , c = \left(\begin{array}{c}2&2&4\end{array}\right)\\\\ \to x^{(k+1)} = \left[\begin{array}{ccc} \frac{3}{4}& \frac{1}{4}& \frac{1}{2}\\ 0 & \frac{1}{2}& 0\\ -\frac{1}{4}& -\frac{1}{4} & 0\end{array}\right] x^k + \left[\begin{array}{c}2&2&4\end{array}\right] \\\\[/tex]
after solving the value the answer is
:
[tex]\lim_{k \to \infty} x^k=o = \left[\begin{array}{c}0&0&0\end{array}\right][/tex]
Related Questions
PLEASE HELP!!!!!!!! ONLY MARKING JWANG BRAINLIEST!
Answers
Answer:
What?
Step-by-step explanation:
Is there an attachment?
Answer:
yes no yes yes
Step-by-step explanation:
please mark me brainliest
Consider the following two loans for P0=$20,000.
Loan A: 10 year loan, annual interest rate of 15%, monthly repayments of $322.67.
Loan B: 8 year loan, annual interest rate of 12%, monthly repayments of $325.06.
On which loan will you pay the least interest?
Answers
A random sample of size 64 was obtained which had sample mean of 1.03 and sample standard deviation of 0.189. Find the P-value.
Answers
Answer:
The P-value is 80.23%
Step-by-step explanation:
Given;
number of samples, n = 64
sample mean, X = 1.03
standard deviation, σ = 0.189
[tex]sample \ mean \ (X) = \frac{Sum \ of \ samples}{number \ of \ samples \ -1} \\\\1.03 = \frac{Sum \ of \ samples}{64 -1}\\\\Sum \ of \ samples = 1.03(63)\\\\Sum \ of \ samples = 64.89[/tex]
Population mean (μ) is given as;
[tex]\mu = \frac{Sum \ of \ samples}{number \ of \ samples} \\\\\mu = \frac{64.89}{64} \\\\\mu = 1.01 \\[/tex]
The z-score is given as;
[tex]z = \frac{X -\mu}{\frac{\sigma}{\sqrt{n} } }\\\\z = \frac{1.03 -1.01}{\frac{0.189}{\sqrt{64} } }\\\\z = \frac{0.02}{\frac{0.189}{8} }\\\\z = 0.8466 \\[/tex]
z ≅ 0.85
From the z-table, the P-value at the given z-score is 0.8023 = 80.23%;
PLEASE HELP!!
Which representation models a proportional relationship between x and y
Answers
Translate the sentence into an inequality.
Ten subtracted from the product of 5 and a number is less than -29.
Use the variable x for the unknown number.
Answers
Answer:
-29>(5*x)-10
Step-by-step explanation:
Answer:
-29 > 5x - 10
Step-by-step explanation:
Since it says PRODUCT in there it means its times
so 5x
x = a number
ten subtracted from that would be
5x - 10
and since its going to be less than -29 that would be <-29
-29 > 5x - 10
sorry if Im wrong
If - 24 = 3(1 + r) what is the value of 7(1 + r)
Answers
Answer:
-9
Step-by-step explanation:
The value of 7(1 + r) is -56.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Given:
- 24 = 3(1 + r)
Now, solving for r
Divide both side by 3
-24/ 3 = 3(1 +r)/3
-8= 1+ r
Subtract 1 from both side
-8 -1 = 1 + r -1
r=-9
Now, 7(1 + r)
=7(1 -9)
=7(-8)
=-56
Hence, the value of 7(1 + r) is -56.
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The Westside Bakery uses 440 pounds of sugar to make
1,000 cakes. Each cake contains the same amount of sugar.
How many pounds of sugar are used in each cake?
A 0.044 pound
B 0.44 pound
C 4.4 pounds
D 44 pounds
Answers
Answer:b) 0.44
Step-by-step explanation:
Why are both of the answers to the last question correct?
Answers
Answer:
Which last question?
Answer:
what question??? there's no image
In the figure AC and BD bisect each other. The length of AB is 12 centimeters and the length of BC is 11 centimeters. The length of AD is ___ centimeters and the length of DC is ___
Answers
Answer:
AD = 11 cmDC = 12 cmStep-by-step explanation:
Triangles AEB and CED are congruent as per SAS theorem since two sides are congruent and included angles are same as vertical angles
Therefore AB = DC = 12 cmSimilarly, BC = AD = 11 cmAnswer: AD = 11 cm
DC = 12 cm
Step-by-step explanation:
LAST QUESTION ANY EXPEETS ON THAT CAN HELP ME OR ACE OR GENIUS?
Answers
Answer:
4.3 cm is the length of the object being measured by caliper
Answer:
D. cm
Step-by-step explanation:
Hope this will help
there are 4750 liters in a hot tub. if 632640 milliliters of water drained out of the hot tub, how many milliliters still remain in the hot tub?
Answers
Solve the proportion below ? 5/x = 1/4
x=_
Answers
Answer:
x=20
Step-by-step explanation:
you just have to take 4 times 5.
1/4 = 5/20
20=x
Answer:20
Step-by-step explanation:
What is the y-intercept of the equation 2x + 3y = 12?
-2/3
12
6
4
Answers
2x+3y-12=0
Step-by-step explanation:
Thats. That. boi. byś.
Answer:
4
Step-by-step explanation:
Replace the x with 02(0) + 3y = 12
Solve3y = 12
4
Hopefully this helps you!!!
Which of the following could be the three angle measures of a triangle?
A. 26°, 17°, 47°
B. 26°, 107°, 47°
C. 26°, 127°, 47°
D. 26°, 117°, 47°
Answers
Answer:
B.
Step-by-step explanation:
The angles of a triangle are supplementary, meaning that they have a sum of 180 degrees. B is the only answer where the angles add up to 180.
26 + 107 + 47 = 180
help plsss?? I rlly need it!!
Answers
Beth has a bag of apples.She gives 6 apples to Natasha.Now she has 7 left.How many apples were in the bag at first?
Answers
Simplify 7 + (−3). (1 point)
a
−10
b
−4
c
4
d
10
Answers
Answer:
C. 4
Step-by-step explanation:
To simplify this expression remember that adding a negative number is the same as subtracting it. So a+(-b)=a-b, this means 7+(-3)=7-3. 7-3 is 4, so C is correct.
What is the value of X?
Answers
Answer:
i think its C but let me know if im wrong
hope it helps!:)
he following formula is used in economics to find a factory's unit labor cost UUU, where OOO is the hourly output per worker and WWW is the hourly compensation per worker.
Rearrange the formula to highlight the hourly compensation per worker. (see attachment)
W =W=W, equals
Answers
Answer:
W = O/U
Step-by-step explanation:
U/1 = O/W
WU=O
W = O/U
The hourly compensation per worker is given by formula W = O/U.
Given,
U = O/W
U = Factory unit cost.
O = Hourly output per worker.
W = Hourly compensation per worker.
Now,
Rearranging to get hourly compensation per worker,
Hourly compensation per worker will be given by Hourly output per worker divided by Factory unit cost.
So,
Formulating the statement into the formula to highlight the hourly compensation per worker.
W = O/U
where,
W = Hourly compensation per worker.
O = Hourly output per worker.
U = Factory unit cost.
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The probability that a certain virus infects a random person is 0.2. If a random sample of 15 people is taken, what is the probability that at least one person is infected?
Answers
Answer:
0.9648
Step-by-step explanation:
Given that:
p = 0.2
Sample size = Number of trials (n) = 15
Probability that atleast one person is infected.
This can be solved using the binomial probability function :
P(x = x) = nCx * p^x * (1 - p)^(n-x)
P(x ≥ 1) = p(1) + p(2) + p(3) +... + p(15)
The sum of the individual probabilities of p(1) up to p(15)
Therefore, to save computation time, we can use the binomial probability calculator :
P(x ≥ 1) = 0.9648
Solve the following equation in slope-intercept form
Answers
Answer:
A. y=7x+18
Step-by-step explanation:
The graph below can be used to help solve which of the following trigonometric inequalities over the interval
0
Answers
Find the surface area
Answers
Answer: 264
Step-by-step explanation:
Ben is twice his brothers age. If the sum of their ages is below 81, how old could bens brother be?
Answers
Answer: Bens brother is dead
Step-by-step explanation:
Sad,sad,sad
Simplify 5^-2 x 5^5 x 5
Answers
Answer:
e
Step-by-step explanation:
2
X+2x+15=5x+5 what is the answer to this question I need so help please and thanks I need it fast as possible.
Answers
Answer:
5 =x
Step-by-step explanation:
X+2x+15=5x+5
Combine like terms
3x+15 = 5x+5
Subtract 3x from each side
3x+15 -3x = 5x+5 -3x
15 = 2x+5
Subtract 5 from each side
15-5 = 2x+5-5
10 =2x
Divide each side by 2
10/2 =2x/2
5 =x
Please help will give brainleist
Answers
Answer:
Y= -1/3x +2.5
step-by-step explanation:
first I reconfigured the given equation: x+3y=15
-x+x+3y=15 -x Subtracted x from both sides
3y=15-x Simplify
3y/3=15-x/3 Divide both sides by 3
y=-1/3x+3 Simplify
I turned it into y=-1/3x+5
then I translated the line up and down to find what point crossed (6,1)
The proper value for B in y=mx+b was 2.5
Try using Desmos online calculator it really helps
Hope this helped :)
Coach McNeil needs 60 bottles of Gatorade for his baseball team's practice. He stops by the store on the way to practice. Food Lion is offering 2 specials: a 10 pack of Gatorade for $12, or a 6 pack of Gatorade for $7.50. Should he buy six of the 10-packs or ten of the 6-packs? Which special offer would be the better deal?
Answers
Answer:
The ten packs
Step-by-step explanation:
If he buys the ten pack, he would spend $72
If he buys the 6 pack, he would spend $75
Therefore, he should buy the ten packs
Help please thank you I appreciate it
Answers
Answer:
Answer A
Step-by-step explanation:
All I had to do was look up a Congruent Figure.
Ann broke up
a large array into two smaller arrays.
The two smaller arrays show 1 X 8 and
4 X 8. What was the large array that
Ann started with?
Answers
Answer:
I think. its below
Step-by-step explanation:
1 x 8 = 8
4 x 8 = 32
If Ann broke up a large array into two smaller arrays. The two smaller arrays show 1 X 8 and 4 X 8 then 40 is Anna started array.
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
Given,
Ann broke up a large array into two smaller arrays.
Th first smaller array show 1 X 8
The second smaller array show 4 X 8.
First smaller array show 1 X 8
=8
Second smaller array show 4 X 8.
32
Now let us add both the arrays
32+8=40
Hence, 40 is the large array that Ann started.
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