1

# Problem 6 Let U be an upper triangular n X n matrix Prove thatK(U) max |Uii|/ min |Uiil 1<i<n 1Ki<nUse this inequality to estimate the condition number ...

## Question

###### Problem 6 Let U be an upper triangular n X n matrix Prove thatK(U) max |Uii|/ min |Uiil 1<i<n 1Ki<nUse this inequality to estimate the condition number of~2 1 0 010 05 6 7 5 10A =Compare with the true condition number of that matrix

Problem 6 Let U be an upper triangular n X n matrix Prove that K(U) max |Uii|/ min |Uiil 1<i<n 1Ki<n Use this inequality to estimate the condition number of ~2 1 0 0 10 0 5 6 7 5 10 A = Compare with the true condition number of that matrix

#### Similar Solved Questions

##### 9 Let AX B where Acos 0 sin 0sin 0 'X = and B Consider the cos 0 cos 0 sin 0 matrices P and Q _ Using the Cramer's rule to solve sin 0 Cos 0 for & and ! we must have:Vep)sto731And the solulion (or and:V is:cos 0sin 0 andcos 0sin 0(C) *sin 0cos 0 and ycOs 0 sin 0(D) rsin Q and % sin Q cos (_(E)CoS
9 Let AX B where A cos 0 sin 0 sin 0 'X = and B Consider the cos 0 cos 0 sin 0 matrices P and Q _ Using the Cramer's rule to solve sin 0 Cos 0 for & and ! we must have: Vep) sto 731 And the solulion (or and:V is: cos 0 sin 0 and cos 0 sin 0 (C) * sin 0 cos 0 and y cOs 0 sin 0 (D) r sin...
##### C) (A -B)xc=(AxC) - (B * C)
c) (A -B)xc=(AxC) - (B * C)...
##### Force E(x,Y,z) =x _yz + cos(z) moves a body along the trajectory given by x=t,y=t,z-nt for 0 <t<3_ The initial point is Pi at location (0,0,0) and the last point of the trajectory is Pz at location (9, 3, 31): What is the work done by moving this body from the terminal position Pz back to the original position P ?
force E(x,Y,z) =x _yz + cos(z) moves a body along the trajectory given by x=t,y=t,z-nt for 0 <t<3_ The initial point is Pi at location (0,0,0) and the last point of the trajectory is Pz at location (9, 3, 31): What is the work done by moving this body from the terminal position Pz back to the ...
##### Use the information below to answer questions 5 _ 6. Please note additional information between the questions to assist you with developing your answers. For the purpose of this question we will assume that in Orpington chickens white feather color is dominant to brown and blue egg color is dominant to white. We will also assume that feather color and egg color are controlled by genes at separate loci on autosomes_ A chicken farmer purchased a cock he believed to be true breeding dominant at bot
Use the information below to answer questions 5 _ 6. Please note additional information between the questions to assist you with developing your answers. For the purpose of this question we will assume that in Orpington chickens white feather color is dominant to brown and blue egg color is dominant...
##### QUESTION 9Consider the linear differential equation y = ~y = 0 */3 with the initial conditlon Mtor Solve the Initial value problem to find the particular solution use it to calculate y(4).Trpe your answer correct to decimal places)d) =
QUESTION 9 Consider the linear differential equation y = ~y = 0 */3 with the initial conditlon Mtor Solve the Initial value problem to find the particular solution use it to calculate y(4). Trpe your answer correct to decimal places) d) =...
##### A few mechanics on a Tovota showroom identified that they attend an average of (# + 4) cars per week: Assume the standard deviation is A random sample of 26 weeks was chosen: Find the 90% confidence interva for mean; (14 Marks)Estimate the 95% confidence interval for the standard deviation ifa research of (A + 8) Chocolate brands shows that the number of A calories as standard deviation for these Chocolate brands Assume the variable is normally distributed: (12 Marks)
A few mechanics on a Tovota showroom identified that they attend an average of (# + 4) cars per week: Assume the standard deviation is A random sample of 26 weeks was chosen: Find the 90% confidence interva for mean; (14 Marks) Estimate the 95% confidence interval for the standard deviation ifa rese...
##### What magnetic field strength and direction will levitate the $2.0 \mathrm{g}$ wire in Figure $\mathrm{P} 24.33 ?$
What magnetic field strength and direction will levitate the $2.0 \mathrm{g}$ wire in Figure $\mathrm{P} 24.33 ?$...
##### Kthe half Iife of a radioactlve substance Is 2 hours and hours have passed, how much of a 700084 will be Jeft (in Ba) after those hours? How many Curies will be left (convert to Guries from Bq and convert to scientifk notation; Thls will be very small numberl) 1Cl-3.7*10"84 (10 points)Pertorm the followlng converslons and convemt your Inater to_Iciantlilanoaatlon: shotl Lworkto tecalve credlf (5 polnts cach, 10 points total) 0.0086 Mcgjgrams - millleroms280,456 mkroliters t0 mlllllters7) LI
Kthe half Iife of a radioactlve substance Is 2 hours and hours have passed, how much of a 700084 will be Jeft (in Ba) after those hours? How many Curies will be left (convert to Guries from Bq and convert to scientifk notation; Thls will be very small numberl) 1Cl-3.7*10"84 (10 points) Pertorm ...
##### Problem 2.(25 points) The differential equationy+4y = (y + )ycan be written in differential fom:M(I, y) dr + N(z,y) dy = 0where M(z,y)and N(z,y)The general solution of the differential equation isNote: You can earn partial credit on this problem.
Problem 2. (25 points) The differential equation y+4y = (y + )y can be written in differential fom: M(I, y) dr + N(z,y) dy = 0 where M(z,y) and N(z,y) The general solution of the differential equation is Note: You can earn partial credit on this problem....
##### Which of the following cannot be made from intermediates of the citric acid cycle?Select one: a. Fatty acidsb. VitaminsAmino acidsd. Glucose
Which of the following cannot be made from intermediates of the citric acid cycle? Select one: a. Fatty acids b. Vitamins Amino acids d. Glucose...
##### 5. How could you synthesize each of these startingmaterials starting from only benzene? Show how you would makeo-chlorotoluene, m-chlorotoluene and p-chlorotoluene
5. How could you synthesize each of these starting materials starting from only benzene? Show how you would make o-chlorotoluene, m-chlorotoluene and p-chlorotoluene...
##### For the following exercises, find the exact area of the region bounded by the given equations if possible. If you are unable to determine the intersection points analytically, use a calculator to approximate the intersection points with three decimal places and determine the approximate area of the region.$$[T]x=e^{y} ext { and } y=x-2$$
For the following exercises, find the exact area of the region bounded by the given equations if possible. If you are unable to determine the intersection points analytically, use a calculator to approximate the intersection points with three decimal places and determine the approximate area of the ...
##### 1. Two equivalents of H2 are needed for the oxidation of benzonitrilea)Trueb) False2. A catalyst is present in the structure of the final product.a)Trueb) False3.For the synthesis of aniline the order of reactions would be 1.Nitration 2.Catalytic reductiona) Trueb) False 4.The reaction intermediate is acidic in character a) True b) False 5. Can aromatic electrophilic substitution reactions occur without a catalyst? a)True b) False 6.F
1. Two equivalents of H2 are needed for the oxidation of benzonitrile a)True b) False 2. A catalyst is present in the structure of the final product. a)True b) False 3.For the synthesis of aniline the order of reactions would be 1.Nitration 2.Catalytic reduction a) True b) False 4.The r...
##### 10. Suppose T: R? _ R? is a linear_ transformation with T '([1) Find [4] andv (II) 7 ((-51); [5}:
10. Suppose T: R? _ R? is a linear_ transformation with T '([1) Find [4] andv (II) 7 ((-51); [5}:...
##### A phone batteryâ€™s (lithium-ion) lifespan has a mean of 257charge cycles, the number of times the phone is charged to fullcapacity, with a standard deviation of 17 cycles. A sample of 58batteries is tested. PART A. What isthe probability of the sample mean lifespans is greater than 261charge cycles? Include a diagram of the curve, identifying wherethe population mean is in comparison to the area of the regionbeing found. PART B. Find the20th percentile of sample mean lifesp
A phone batteryâ€™s (lithium-ion) lifespan has a mean of 257 charge cycles, the number of times the phone is charged to full capacity, with a standard deviation of 17 cycles. A sample of 58 batteries is tested. PART A. What is the probability of the sample mean lifespans is greater ...