1

# B) Prof: X has two brilliant students Y and Z in his class. He introduces the concept of vector spaces, bases and dimension in his 3rd session_ As an exercise, he g...

## Question

###### B) Prof: X has two brilliant students Y and Z in his class. He introduces the concept of vector spaces, bases and dimension in his 3rd session_ As an exercise, he gives a vector space V of dimension n and asks Y and Z to find the basis based on the following: Y should start with a set S which has a single non-zero element of V and build the basis by adding vectors to S such that S is linearly independent. The process should be stopped once S has n elements. 2 is asked to start with a set T which

b) Prof: X has two brilliant students Y and Z in his class. He introduces the concept of vector spaces, bases and dimension in his 3rd session_ As an exercise, he gives a vector space V of dimension n and asks Y and Z to find the basis based on the following: Y should start with a set S which has a single non-zero element of V and build the basis by adding vectors to S such that S is linearly independent. The process should be stopped once S has n elements. 2 is asked to start with a set T which has more than elements, say n + k, with k > 0, and remove elements such that T becomes linearly independent. The next day Y and Z bring in their working: Prof: X asks the class if S and T, in the working of Y and Z, the same sets? While student U says yes, student W says need not and Prof: X says that both U and W could be correct Justify the statement of Prof. X with suitable examples of V, S and T. (4

#### Similar Solved Questions

##### The perimeter of a triangular plot of land is 2040 feet. The longest side is twice thc length oft shortest side, and the middle-length side is 200 fcet more than the shortest side: What i thc length of the shortest side of the plot of land? Use an cquation or system of equations t0 solve this problem and show Your work . Identily Points} label any variables you use with diagram andlor with words:2040f+ 2x 22X+ 260
The perimeter of a triangular plot of land is 2040 feet. The longest side is twice thc length oft shortest side, and the middle-length side is 200 fcet more than the shortest side: What i thc length of the shortest side of the plot of land? Use an cquation or system of equations t0 solve this proble...
##### Yet Lered d out ofWhich of the following ; false Select = about one:, RNA 'synthesis? tinvolves synthesis it occurs the 3' in the to 5' c it nucleus direction involves of ' splicing eukaryotes it requires RNA eukaryotes, polymerase but uracil is not: 'used linstead prokaryotes of thymine during elongationSlidesJumpNext pageSupr
Yet Lered d out of Which of the following ; false Select = about one:, RNA 'synthesis? tinvolves synthesis it occurs the 3' in the to 5' c it nucleus direction involves of ' splicing eukaryotes it requires RNA eukaryotes, polymerase but uracil is not: 'used linstead prokary...
##### The 04 3 Wl 1 WU IOXSUP 3 WH Type your L' HH the V 1 answer velocity Intetval molation zero IS 1 IL Use a comIa 1 0 t0 separate soparalo soparate answers as 1 answers needed ) needed ) needad )
The 04 3 Wl 1 WU IOXSUP 3 WH Type your L' HH the V 1 answer velocity Intetval molation zero IS 1 IL Use a comIa 1 0 t0 separate soparalo soparate answers as 1 answers needed ) needed ) needad )...
##### MATIBAD2323 Statistics VSO1 (1)QuandHomework: Practice Test 4 Ch; 9 IS ari Score: 0 of 22 of 25 (25 complete) 9.1.1e Tel If you use 0.05 level significance in (two-tail) hypothesis test; what will you decide i ZSTAT = +2.14. Click there toview page of the cumulative_standardized normal Click here_to view page distribulion table; of lha cumulalive slandardized_normal dislrbulion table; {Reoemmine the decision rule: Select the correct choice below &nd fill in ! 6 (211 (Round to throo decimal p
MATIBAD2323 Statistics VSO1 (1) Quand Homework: Practice Test 4 Ch; 9 IS ari Score: 0 of 22 of 25 (25 complete) 9.1.1 e Tel If you use 0.05 level significance in (two-tail) hypothesis test; what will you decide i ZSTAT = +2.14. Click there toview page of the cumulative_standardized normal Click here...
##### A 2100 bp plasmid DNA (average twist angle of 34.3"/bp) has a superhelical density of-0.05_What are the values of L, Tand W for this DNA molecule? Show the calculations for how you derive your answers_ (4.5 points) T= 210 LO= 2100/10.5 200 W= -10 W= N x Sigma /10.5 = 2100(-0.05) 10.5 =-10 L=200 T=200 - (-10) = 210b) What would be the values of L, Tand W for this molecule after treatment with limiting amounts of Gyrase (such that each molecule is only affected by the gyrase once) in the abse
A 2100 bp plasmid DNA (average twist angle of 34.3"/bp) has a superhelical density of-0.05_ What are the values of L, Tand W for this DNA molecule? Show the calculations for how you derive your answers_ (4.5 points) T= 210 LO= 2100/10.5 200 W= -10 W= N x Sigma /10.5 = 2100(-0.05) 10.5 =-10 L=20...
##### 17_ Prove that Iax6f-a11ff -(a.6)
17_ Prove that Iax6f-a11ff -(a.6)...
##### (13 points) Let and - be circles centered origin in the plane (3 points) Suppose circle has J radius of 4 units_ Ifan arc on has a length 0f 14 unns what is the measure radians, of the JnEle centered at the origin that encloses this JrC:(4 points)_ classmate sketches the angle tound pun a starting from the positive I-axis and ending ovadrini this an accurate sketch of the angle? Justify your answyerpoints) Ifthe same angle from part a. enclosed an arc on cirdle_ that measures 22 units Iong what
(13 points) Let and - be circles centered origin in the plane (3 points) Suppose circle has J radius of 4 units_ Ifan arc on has a length 0f 14 unns what is the measure radians, of the JnEle centered at the origin that encloses this JrC: (4 points)_ classmate sketches the angle tound pun a starting ...
##### Section 6.5 Singular Value Decomposition: Problem 2 Puvicus PublaI Ptublem List Next ProblemnResults tor this submissionEcterednAnswver PrevicwPerlncomecncdrieciinconectncomectcuWECIHncnnertncomeccutEHcdticiAtleast cne oftne answers abeie NCT contect ofthe questions remains unansreredmuimtaa riyulai vaalte dAIensfceneolamaxlollc ts_EsEsTn.i ~08 | 0.6~035 ~05Find thc cbsest (wilh respcctFrobcnius noln) matx ol TankFind thc Frobcnius nOrm 0l 4 AlIlv
Section 6.5 Singular Value Decomposition: Problem 2 Puvicus PublaI Ptublem List Next Problemn Results tor this submission Ecteredn Answver Previcw Perl ncomec ncdrieci inconect ncomect cuWECI Hncnnert ncomec cutE Hcdtici Atleast cne oftne answers abeie NCT contect ofthe questions remains unansrered ...
##### Specify whether the structures below have - chirality center: (Other terms for chirality center include stereocenter; stercogenic center and chiral center )OH
Specify whether the structures below have - chirality center: (Other terms for chirality center include stereocenter; stercogenic center and chiral center ) OH...
##### Find the accumulated present value of an investment for which there is perpetual continuous money flow of S3800 per year at an interest rate of 6%, compounded continuously:The accumulated present value is (Type an integer or decimal rounded to the nearest hundredth as needed )
Find the accumulated present value of an investment for which there is perpetual continuous money flow of S3800 per year at an interest rate of 6%, compounded continuously: The accumulated present value is (Type an integer or decimal rounded to the nearest hundredth as needed )...
##### Why don't any of the methods for establishing distances to galaxies, described in Galaxies (other than Hubble's law itself), work for quasars?
Why don't any of the methods for establishing distances to galaxies, described in Galaxies (other than Hubble's law itself), work for quasars?...
##### QUESTION[4 Marks]A shop manager observed the number of shoes sold X1) variation in price (Xz, in rands the advertisement costs in local newspapers (Y3, in rands) and the presence of a sales assistant (Y4, in hours per period) over 10 different periods. The information is summarised using the fol- lowing data matrix. 230 125 200 109 181 99 55 107 165 97 105 98 150 115 85 81 97 120 192 100 150 103 181 80 85 93 189 90 120 172 95 110 86 170 125 130 78 Use the above data matrix to find the empirical:
QUESTION [4 Marks] A shop manager observed the number of shoes sold X1) variation in price (Xz, in rands the advertisement costs in local newspapers (Y3, in rands) and the presence of a sales assistant (Y4, in hours per period) over 10 different periods. The information is summarised using the fol- ...
##### The position of an object is givenby x = 3.5 m sin (21radÃ—s-1 t),where t is time in seconds.What is its maximum acceleration?3.5 m/s274 m/s2440 m/s21500 m/s26.0 m/s20.17 m/s22.9 m/s20.0079 m/s221 m/s2
The position of an object is given by x = 3.5 m sin (21 radÃ—s-1 t), where t is time in seconds. What is its maximum acceleration? 3.5 m/s2 74 m/s2 440 m/s2 1500 m/s2 6.0 m/s2 0.17 m/s2 2.9 m/s2 0.0079 m/s2 21 m/s2...
##### The vector field F is shown in the xy plane and looks the same in all other horizontal planes.Y 2Is div F positive, negative, Or Zero?PositiveNegative ZeroQuestion 24. Points possible: This is attempt of 1_Find the flux of the vector field F (y, 0, 1) across the part of the plane z = 2 + 3r + 2y above the rectangle [0, 4] [0, 2] with upwards orientation480-160-32
The vector field F is shown in the xy plane and looks the same in all other horizontal planes. Y 2 Is div F positive, negative, Or Zero? Positive Negative Zero Question 24. Points possible: This is attempt of 1_ Find the flux of the vector field F (y, 0, 1) across the part of the plane z = 2 + 3r + ...