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# Let $B$ be a fixed matrix in $M_{n}(\mathbb{F})$, where $\mathbb{F}$ is an arbitrary field. Define $T: M_{n}(\mathbb{F}) \rightarrow M_{n}(\mathbb{F})$ by $$T(A)=A... ## Question ###### Let B be a fixed matrix in M_{n}(\mathbb{F}), where \mathbb{F} is an arbitrary field. Define T: M_{n}(\mathbb{F}) \rightarrow M_{n}(\mathbb{F}) by$$ T(A)=A B-B A . $$Prove that T is a linear operator on M_{n}(\mathbb{F}) . Describe the kernel of T if B is scalar matrix. Find the range of T in case B is a diagonal matrix. Let B be a fixed matrix in M_{n}(\mathbb{F}), where \mathbb{F} is an arbitrary field. Define T: M_{n}(\mathbb{F}) \rightarrow M_{n}(\mathbb{F}) by$$ T(A)=A B-B A .  Prove that $T$ is a linear operator on $M_{n}(\mathbb{F}) .$ Describe the kernel of $T$ if $B$ is scalar matrix. Find the range of $T$ in case $B$ is a diagonal matrix. #### Similar Solved Questions

##### X _ 64 Find all the vertical asymptotes (if any) of the graph of the function f (x) = x-4 A_ x} _ 64 The graph of the function f (x) has no vertical asymptotes_ X-4 B. x =- C. *=-4,4 D. x =-64 E. x=4
x _ 64 Find all the vertical asymptotes (if any) of the graph of the function f (x) = x-4 A_ x} _ 64 The graph of the function f (x) has no vertical asymptotes_ X-4 B. x =- C. *=-4,4 D. x =-64 E. x=4...
##### The stock prices of Lwo COI[Ilies at (he ec of aY given yCAI TL( mOdeled wibh TandOI Variables. X ad that follow distribbion with joint dcnsiby [HcLion:
The stock prices of Lwo COI[Ilies at (he ec of aY given yCAI TL( mOdeled wibh TandOI Variables. X ad that follow distribbion with joint dcnsiby [HcLion:...
##### 7.71 7U2 I:04 EXc 1:04 .r.inirmobilyhilgll JSOivevde +
7.71 7 U2 I:04 EXc 1:04 .r.inir mobily hilgll JS Oivevde +...
##### NAME CALCULAIION ASSIGNMENI MQLAR_MASS Calculate the molar mass of_each substance listed below: 1) CQ2 2) CzHso 3) Y2" (MoOj3 Be3 Nz NazS04 NaHcog 7) (NH_ '42C4H49 8) WA (Fe(CN}l3Hzo 10) C3ts0
NAME CALCULAIION ASSIGNMENI MQLAR_MASS Calculate the molar mass of_each substance listed below: 1) CQ2 2) CzHso 3) Y2" (MoOj3 Be3 Nz NazS04 NaHcog 7) (NH_ '42C4H49 8) WA (Fe(CN}l3 Hzo 10) C3ts0...
##### IRINMR  Unknown Spectra #@ Molr = [ASt 174.19 %( 562 "H 8.10LCioyThe lower spectrum in the 11O0-1500 cm"' region simply stronger fingerprint region _highlight
IRINMR  Unknown Spectra #@ Molr = [ASt 174.19 %( 562 "H 8.10 LCioy The lower spectrum in the 11O0-1500 cm"' region simply stronger fingerprint region _ highlight...
##### 13. Vis the solid bounded above by the hyperboloid 2? = 4+5(22 + y?) , bounded below by the cone =2Vr? +y2 and inside the cylinder 1? | y? = 1. IfJ =III c (4- 1) dV 9t_ Then using Gauss' divergence theorem evaluate the following surface integral:M =fI [(ssinh I + 20y? + 22) i+ (cy 3y cosh T 2yz (522 J13 + 21 y7)ndS;where the closed surface S bounds the region V and n is the outward normal to S Use Gauss" divergence theorem to convert the surface integral to volume integral_
13. Vis the solid bounded above by the hyperboloid 2? = 4+5(22 + y?) , bounded below by the cone =2Vr? +y2 and inside the cylinder 1? | y? = 1. If J = III c (4- 1) dV 9t_ Then using Gauss' divergence theorem evaluate the following surface integral: M = fI [(ssinh I + 20y? + 22) i+ (cy 3y cosh T...
##### DeaLTanbttun0.085 mignabc leld:magnctic through thne cl Unitsrectanguler koop wilh sdes cm a1 ,pliced walholanoJCr{005
deaL Tanbttun 0.085 mignabc leld: magnctic through thne cl Units rectanguler koop wilh sdes cm a1 , pliced walh olano JCr{005...
##### Suppose that X has the uniform distribution on the interval [0. 5] and that the random variable Y is defined by Y =0 il X<LY= if X>3 and Y =X otherwise: Sketch the cdf o Y.
Suppose that X has the uniform distribution on the interval [0. 5] and that the random variable Y is defined by Y =0 il X<LY= if X>3 and Y =X otherwise: Sketch the cdf o Y....
##### Wukho thetelowing#tn 0l Une Gen cheieel Chootd= that acol IAGaonibien- excmoltv Ihakkhiznehren} & not ingenetic trke (txy are Kentical but hae d m. edantatsre onicobreni not Inllucncedby Iia hcasu Lult- enmplty that ichizoontyae at pcaee putly on ronn) edeo halet Kecnt Jhsuie unonainc CrrKnshtcrs mevhje
Wukho thetelowing#tn 0l Une Gen cheieel Chootd= that acol IAGaonibien- excmoltv Ihakkhiznehren} & not ingenetic trke (txy are Kentical but hae d m. edantatsre onicobreni not Inllucncedby Iia hcasu Lult- enmplty that ichizoontyae at pcaee putly on ronn) edeo halet Kecnt Jhsuie unonainc CrrKnshtcr...
##### Are ONLY found in cardiac muscle; Intercalated discsUninucleiMultiple nucleiStriations
are ONLY found in cardiac muscle; Intercalated discs Uninuclei Multiple nuclei Striations...
##### 0A 1 7.3.25 Oezm %h4 2 Dt 34 cli Compldlc puli Homework: GuisuenheCuo) 20221Sp19 L 1 3 7.3 and Ha Choose tne CdEc[ anstel Delo; 3 1 1 3 8 8 1 =005, #ulgr Ian 1 Vv-eIlcen Cobos dovounao cnouan #hcULo WncOn lCcouit MH 1 Score: Question Help 1 1 1
0A 1 7.3.25 Oezm %h4 2 Dt 34 cli Compldlc puli Homework: GuisuenheCuo) 20221Sp19 L 1 3 7.3 and Ha Choose tne CdEc[ anstel Delo; 3 1 1 3 8 8 1 =005, #ulgr Ian 1 Vv-eIlcen Cobos dovounao cnouan #hcULo WncOn lCcouit MH 1 Score: Question Help 1 1 1...
##### Point) In this problem you will use undetermined coefficients to solve the nonhomogeneous equation Y' + 6y + 9y = - (18te 3t + 4e-3t +9t + 24)with initial valuesy(0) 73 and Y (0) =A Write the characteristic equation for the associated homogeneous equation. (Use r for your variable )12 + 6r + 9 = 0B. Write the fundamental solutions for the associated homogeneous equation:Y1~3t)Y2-3t ) teC. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coef
point) In this problem you will use undetermined coefficients to solve the nonhomogeneous equation Y' + 6y + 9y = - (18te 3t + 4e-3t +9t + 24) with initial values y(0) 73 and Y (0) = A Write the characteristic equation for the associated homogeneous equation. (Use r for your variable ) 12 + 6r ...
##### You are using a bicycle pump to fill a bicycle tire with air. It gets harder and harder to push the plunger on the pump the more air is in the tire. Explain what is going on.
You are using a bicycle pump to fill a bicycle tire with air. It gets harder and harder to push the plunger on the pump the more air is in the tire. Explain what is going on....
##### Solve the following problem: ð‘€ð‘Žð‘¥ ð‘“ (ð‘¥, ð‘¦) = (5 - ð‘¥) ð‘¥ + (10 - ð‘¦)ð‘¦ - (ð‘¥ + ð‘¦) 2 ð‘†. ð‘Ž. ð‘¦ â‰¤ 2, ð‘¥ + ð‘¦ â‰¥ 7/2
Solve the following problem: ð‘€ð‘Žð‘¥ ð‘“ (ð‘¥, ð‘¦) = (5 - ð‘¥) ð‘¥ + (10 - ð‘¦) ð‘¦ - (ð‘¥ + ð‘¦) 2 ð‘†. ð‘Ž. ð‘¦ â‰¤ 2, ð‘¥ + ð‘¦ â‰¥ 7/2...
##### Cetait raoid covid lest used on person experiencing covid-19 Symptoms has sensitivity 79% and speciticity 97.996 . Tat_ porson who truly has covid when the lest/ given t0 contes back positivo 7996 0f th# { me, and when - given t0 soieone wha truly docsn " negalive 97,998 0i the Lun have covid cotus backJuan does not have any known covid exposure, but Fe' developed cough He doubts t'$covia, but ho knows there$ sone chance; which he estimaies 10%6, He gets rapid test ad conio# b
cetait raoid covid lest used on person experiencing covid-19 Symptoms has sensitivity 79% and speciticity 97.996 . Tat_ porson who truly has covid when the lest/ given t0 contes back positivo 7996 0f th# { me, and when - given t0 soieone wha truly docsn " negalive 97,998 0i the Lun have covid...