3

DimensionFundamental matrix spaces, rank; and nullity (parts 1 and 2) Change of basisFor each of the linear systems below_(a) Find a basis for the subspace of R3 wh...

Question

DimensionFundamental matrix spaces, rank; and nullity (parts 1 and 2) Change of basisFor each of the linear systems below_(a) Find a basis for the subspace of R3 which consists of the solutions of the linear system_ (b) Compute the dimension of the solution space.I +y - 2 = 0 21 9 + 22 =0 ~I+2I - 3y + < 21 _ 6y + 22 31 9y + 32

Dimension Fundamental matrix spaces, rank; and nullity (parts 1 and 2) Change of basis For each of the linear systems below_ (a) Find a basis for the subspace of R3 which consists of the solutions of the linear system_ (b) Compute the dimension of the solution space. I +y - 2 = 0 21 9 + 22 =0 ~I+2 I - 3y + < 21 _ 6y + 22 31 9y + 32



Answers

Find the change-of-basis matrix $P_{B} \leftarrow c$ from the given basis $C$ to the given basis $B$ of the vector space $V.$ $V, B,$ and $C$ from Problem 21.

Okay for this question. They want us to find a basis for a subspace of our three. And by three factors. The span 101 011 and t zero. Thank you. Well, Stephanie gonna be degree three or less, but actually, we see that two of these vectors aren't even linearly independent. This one's just two times that basis. So it's not adding any new information. No new possibilities. Why don't we take a linear combination? Uh, these three effective? Yes. So we can actually just throw this one out and only these to provide new information. It will make a new vector reachable in the spent. So our basis will be 101 and 011 awesome.

Welcome to liberate in the current problem. We are given the equations. Excellent. Plus X two -X. Tree is equal to zero. The next depression is minus two. Excellent. Plus X two x two. Yes. Yes. Yeah. Yeah. That is Monye 6 1. That's extremely It goes to no he has from the this is that is the set of vectors that can generate the uh if you have those victors, you can generate any victor in that vector space. The first thing that we do is we write the argument. The Coefficient Matrix that is 1, 1 minus one -2 -1, two -10. But so this is the coefficient metrics. Now we will do standard reduction of operations. And we started by we start by doing a new second rope. That will be two times old. First through Plus the old 2nd drop. Okay, so we will get This into two,: -20. This into two to minus 11 the center to minus two plus two zero. And a new artery. That would be simply addition of all that one and all our three. So we will have minus one plus 101 plus 00 minus 11 oh one. Class zero one and -10. Now if you see both the second and do our thing so we can do one more this. Uh huh 010. And we didn't subtract recorded all from New R three would be our 1- archery correct? So we get this so if we again go back to the same equation for medical building X one plus X two minus X three is equals to zero and X two equals to zero. So first thing we have is extra equals to zero. Now if this is a question one from one we have X one plus zero minus extreme is equals to zero. Therefore X one minus extra is equals to zero. Therefore X one is equals to extreme. This is another inspiration. Now taking help of this and this. What we can do we can think of a basis vector which is the solution of this basis victor. Well B uh huh solution of the given set. It's given set Only this set marked by one. well marked by one. Whatever it is, it is actually the original set over here. Right? So indeed this Exxon extract through whatever we will find out to be will be solution to. That's it. Now if I as you X one equals three X three and X two is equal to zero. This is there already. And if I just as you knit X one, B. T. Any beard he belongs to the real line. Then extra is also T. Therefore the victor. The solution victory would look like X one comma X two comma X three will be T comma zero committee Credit. So if I take the common we will get 10. That means what? This shows the victor. 101 forms the basis of the given system. Are given system of equations. Okay? And The dimension since there is only one letter and since dad is only thank you since there is only one victor. The dimension. Yes. What? So I hope you could understand this. Let me know if you have any questions but by


Similar Solved Questions

5 answers
Cenide "pownvn chareqie plncco etdhe Orgm andaregelive cnre 4n H0 plcrd Uuta find the Dostion , (incin) benteon (te Olurtes Earotol Hecn
Cenide "pownvn chareqie plncco etdhe Orgm andaregelive cnre 4n H0 plcrd Uuta find the Dostion , (incin) benteon (te Olurtes Earotol Hecn...
5 answers
Methane erd (hlorine Teact to form chloroform &nd hycrogan chlorice, Ike this: CH (g)-JC1,(9) - CHCI;(9) + JHCIg)Tre reacuon Cxornctitoc, 4jco5e mlxture 94 CH, Cl,, CHCI, and HCIhaS cora ~cquiibnum In * Doscd Icaftion Vessel _ Pred d nnJt Onjngc; M jni; pertlrozuont jca* Cabsc thc comcos L on Ehe mixture Inc cISl Also Ctjt" Wnc*nC: Uht cocivdojm shins Ene nght Or ierd;pettlruauencnan omacalnonocuuibticnOro u rgnOnerruteturIta CItu_rAtf HCIM V >lc ^ |
Methane erd (hlorine Teact to form chloroform &nd hycrogan chlorice, Ike this: CH (g)-JC1,(9) - CHCI;(9) + JHCIg) Tre reacuon Cxornctitoc, 4jco5e mlxture 94 CH, Cl,, CHCI, and HCIhaS cora ~cquiibnum In * Doscd Icaftion Vessel _ Pred d nnJt Onjngc; M jni; pertlrozuont jca* Cabsc thc comcos L on E...
5 answers
5 Find the El math derivalive 0 of 1 pt Homework: 8 where 8 Section cos (3x) cos (4y) 13_ 01 sin (3x) sin (4y) , andz Homework 3x + 4y.
5 Find the El math derivalive 0 of 1 pt Homework: 8 where 8 Section cos (3x) cos (4y) 13_ 01 sin (3x) sin (4y) , andz Homework 3x + 4y....
5 answers
Calculate the amount of heat needed to boil 139_ of hexane (CH,4), beginning from temperature of 61.9 * Be sure your answer has unit symbol and the correct number of significant digits
Calculate the amount of heat needed to boil 139_ of hexane (CH,4), beginning from temperature of 61.9 * Be sure your answer has unit symbol and the correct number of significant digits...
1 answers
Theorem l: Let p njkez where 1S prime I p | n, and n = jk and pf j then p
Theorem l: Let p njkez where 1S prime I p | n, and n = jk and pf j then p...
4 answers
Question 10 (1 point)cell is 2N-4, choose the correct stage of division depicted in the imagemetaphasemetaphase Ilmetaphase (mitosis)prophase
Question 10 (1 point) cell is 2N-4, choose the correct stage of division depicted in the image metaphase metaphase Il metaphase (mitosis) prophase...
1 answers
Let $E$ be any event in a sample space $S .$ a. Are $E$ and $S$ mutually exclusive? Explain your answer. b. Are $E$ and $\varnothing$ mutually exclusive? Explain your answer.
Let $E$ be any event in a sample space $S .$ a. Are $E$ and $S$ mutually exclusive? Explain your answer. b. Are $E$ and $\varnothing$ mutually exclusive? Explain your answer....
5 answers
Moving to another questlon will save this response:uestion 10Given Ax)=x_9x? + 1Sx+30 andd(x)=(x-5).Dlvide Plx) by d(x) using syniholle division Iona dlvision Ilnd Q(x) and R(X) Ihen expross P(x) In the form Ptr} dorJotx) Rin) A: P(x}= (x - Skr^2. 5)' (510B, Ptn- ( = 514*2 4k251+ 5C P(x) = (K 5k+42 14x + 85) ' ( 3951D P(x)SK*t2-4-51 - 55Moving to another question wvill euve [ns rosponiee;
Moving to another questlon will save this response: uestion 10 Given Ax)=x_9x? + 1Sx+30 andd(x)=(x-5). Dlvide Plx) by d(x) using syniholle division Iona dlvision Ilnd Q(x) and R(X) Ihen expross P(x) In the form Ptr} dorJotx) Rin) A: P(x}= (x - Skr^2. 5)' (51 0B, Ptn- ( = 514*2 4k251+ 5 C P(x) =...
5 answers
What is the major product formed after the following reactions?LDA MF -70 %2 Chy
What is the major product formed after the following reactions? LDA MF -70 % 2 Chy...
5 answers
Find f (x) for the given function;4 flx) 8 -Xf(x)
Find f (x) for the given function; 4 flx) 8 -X f(x)...
5 answers
Find the limit (if it exists) _ (If an answer does not exist; enter DNE:)Iim(x,P)- (9,9) x2 + y2Enter fraction, integer; exact decmal: Do not approximate. Dlscuss thercontinulcy orther runnictioncontinuous everywhere except x =continuous everywherecontinuous everywhere except (0,continuous for x + Y 2 0continuous only when x +Y >
Find the limit (if it exists) _ (If an answer does not exist; enter DNE:) Iim (x,P)- (9,9) x2 + y2 Enter fraction, integer; exact decmal: Do not approximate. Dlscuss thercontinulcy orther runniction continuous everywhere except x = continuous everywhere continuous everywhere except (0, continuous fo...
5 answers
EEane [enijueuaoceochrideMeoadihydroxyacetorz ribosethesimplestaldosethe simplestketoxgtucoseElyceraldehydepentose1 potnt whichstatements aretrue regarding the monosaccharide below? (Check all that apply } CH-OH C=o HO= Lh OHChOH iEs chemical formulais CsHioos ithzs five chirality centerz itisanaldose this is 2 Haworth projection itisa Dsugar itKahense
EEane [enijueuaoceochride Meoa dihydroxyacetorz ribose thesimplestaldose the simplestketox gtucose Elyceraldehyde pentose 1 potnt whichstatements aretrue regarding the monosaccharide below? (Check all that apply } CH-OH C=o HO= Lh OH ChOH iEs chemical formulais CsHioos ithzs five chirality centerz i...

-- 0.064699--