5

Q2a) LSiIA matrI Verify whether Mir Msa with T(B) BA Mneal tranSormatio unete Mrg dlenotes the set of all matrices. b) Let T R' hxee linear and suppose that ...

Question

Q2a) LSiIA matrI Verify whether Mir Msa with T(B) BA Mneal tranSormatio unete Mrg dlenotes the set of all matrices. b) Let T R' hxee linear and suppose that T((1, ~1)) =(-1,-1,3) ad T((-2.1,0)) F4. ccruc T((1.3 [rom the given data. Is thi: value unique? Justily: (1+1) Verify that Rank-Nullity theorem for the linear transformation T : R' R' defined by T(r1.f2.1i.f4) 202 323).

Q2a) LSiIA matrI Verify whether Mir Msa with T(B) BA Mneal tranSormatio unete Mrg dlenotes the set of all matrices. b) Let T R' hxee linear and suppose that T((1, ~1)) =(-1,-1,3) ad T((-2.1,0)) F4. ccruc T((1.3 [rom the given data. Is thi: value unique? Justily: (1+1) Verify that Rank-Nullity theorem for the linear transformation T : R' R' defined by T(r1.f2.1i.f4) 202 323).



Answers

Determine the matrix representation $[T]_{B}^{C}$ for the given linear transformation $T$ and ordered bases $\bar{B}$ and $C$. $T: P_{2}(\mathbb{R}) \rightarrow \mathbb{R}^{2}$ given by $$T\left(a+b x+c x^{2}\right)=(a-3 c, 2 a+b-2 c)$$ (a) $B=\left\{1, x, x^{2}\right\} ; C=\{(1,0),(0,1)\}$ (b) $B=\left\{1,1+x, 1+x+x^{2}\right\} ; C=\{(1,-1),(2,1)\}$

Okay, first transformation T one, We have matrix a Now, to get to find the colonel. We first reduce this in tow R e f, which means for and for a is takes one simple operation we for the second row, we subtract two of the first from 1 to 2, and it gives us one minus 100 Then that we then that means that X might that why isn't free variable and X men and, uh, any vector were X minus y equals zero then had then makes, uh, a codas here is on the back of a session. It goes to zero. So this is a colonel space of a Why? Why? Because ax equals why? Yeah, se. And same thing with that being, we need a few more operations. So for the 1st 1 we get, he simply switched easily. Switch these two rows around. Then we subtract the first row or the first road by the second role, giving us one minus 2 to 1. And then, uh, the second road twice attracted means attract twice by the first Roque. And that's one minutes to 05 Just by the second by five against one minus two was your one and then subtract the first roll twice by the second giving us the identity matrix. And then that simply means that the Colonel is just going to be the vector zero. Because no other, no other is going to work for them for find the best kernel of t one t two. First we get first, we find 22 just 80 and find the first vector in a B. We get me the time three times the first row and a by the first column and be too time to minus 31 times three and then so on. And then for the second calling, we have one times one plus minus one times minus one equals 200. So long And then we get this matrix and very simple way. Add second row twice by the first, giving us minus 1200 and then me times first road by minus one and it gives us one minus 200 And so that gives 10. So then then then that this is the area. And so we get the equation X minus two white was no. And then this is going to be the colonel to Why? And common line, We're wise element. Same thing for T two t one is at this times be a similar operation for the 1st 1 Oh, to times one plus one time to for and then two times minus one plus mice to use my four. So on get way that we then get this matrix and again. Very simple. We switched the out We switched the rose around subtract by the second row by four of the first row giving us this in the artery f and still in ST Same thing for our first. Our first question is X minus Y equals zero And that is why why earlier? And this is the kernel of t two t one.

Problem number five Uh, a a and that the I wanted you. You ends. And you this sequence one and one and e zero and zero. What? A hero is equal to zero and zero anti. Uh, zero f y 00 is equipped to here and here And the, uh you know, And you you and one is equal to run in one. So we need to ensure that t e 11 he went toe to toe as a mere combinations are better from seeing for we can write that a t Well, e one morning is equal to she's one and one sequent through one times when in the U plus u times run one similarly t Oh, yeah. One and two equals zero is equal to zero times one and zero plus zero times. You know, one de off. Yeah, 21 which can be written as zero times one into you, plus one times you don't want zero. This is zero. What? Toby zero interior and finally see, uh, a two to is equal. One wanted you, Los One deal And I want to get what I'm one. So here this good fishing can be written so that d off B and C is equal to one and one zero and zero, 010111 and just work with Cheney for which in and be the T talk, they get the one to get to get it. School negative. Three. Is it going through? Negative for And get a four. That the one it wanted to is equal to three and three. That he zero to anything. Three and negative, too, is equal to negative two and negative that the you have one, four and zero. It's equal to your ante here. Now we need to show that these thieves as a linear combination or better from C so negative for him. Four can be rated as negative for him for two years. The if the 1st 2 year can be written negative for him for can be written as negative for times one in here, minus four. I'm you know, similarly similarly, this just three and three can be written as three Blind Boy one and zero love 3 a.m. up by buys, you know, horn here and be written and as negative, too. Look, the blind by one and zero plus negative, too. What's the buying by, you know, and one. And finally this cabinet the next here are not buying by one. And here lost zero left buying binds. He ran at one so but the for A B and C is equal to get the court of negative or to be in three take a typical ending at the Pool zero Andy.

Corresponding to t one and t two, that is, we're just multi play David Lee. And this is a quartile producto fan. Be which is a little You just multiply the two matrices. Oh, so the fourth century is minus one times one, which is minus one plus minus four, which is minus way. Second injury is minus five Thought entries one and last entry is with Dean. Now, to find out Tito with the one just multiply, baby they so you will get the falling metrics. It is a quartile 14 seven do in the last two entries minus four. So as you can see, these stool compositions are not seem because even because if they were equal, the images of each of the vectors would be equal like they would send. I liked even after you two off We should be quantity to be one off me For every victory in our but the one Pito off one gonna zero. As you can see, it's just minus right. Come on, one that is the first column off your matrix. But do you do do you? Enough. The same victor is for the in Goma do which which are different vectors. So they're not seem

Problem Number two, which is a weavers, say that T one is equal to one I love plus Dean Wax. Last year, experts so secret one mind the three times zero and two times one plus zero mind it's true times here which you will be equal to 1 to 40 x we have here at X quarter fission which is corresponding to zero minus three times zero and two time zero plus one minus two times here was will be equipped to bear in mind for the X Square. So here we have only expert proficient and this will give and get it to be ending it too. Ah to show that ah, he won and the ex ante expert are at Landry combinations. So we can in a t 11 times one and deal plus two times you're at one anti NCC 20 time is one and zero plus one times you don't want and t X squared is equal to negative one and zero plants negative to zero in one we give negative three and bigots too as shown here So we can say that t one. Oh, see what I wanted to feel the access that you don't want. It's a square in dentistry and negative tour, so that tee off CMB is one of 201 and negative three and against similarly, for a coaching be we say that you want as we to hear it wanted to the same this year. 41 plus X Here we have Moscow efficient on eggs and it gives one and three and one exports X square. So here we have three coefficients here is it's one. So this gives begins and what we have to throw that t one and t one plus X and 31 plus X perfects. It is where it is on any recombination or better see So here we can see that t one which is equal to one to acquit toe a a month the blind by one and negative one plus B month buying by toe and one by solving these equations which gets from here we say that a is equal to negative one and music which one? Eso Similarly using this approach, we can get a bad T one plus acts. They would donate 5/3, uh, one and negative one plus 4/3 21 C plus one x x squared to go negative for entry one the negative one minus one on +13 21. So TCF be one on one with the fiber. Three over. 4/3 but the forward three over negative one over three.


Similar Solved Questions

5 answers
10) Find the first derivative of the function using any technique:f(x)V(x? Sx
10) Find the first derivative of the function using any technique: f(x) V(x? Sx...
5 answers
Wd0 w88 14x Jiz 1041517 1 = and box of 3 5470,170 14 W 170 DVDs the worth worth 38 0 DVDb, box contains 1 systeonef 82 W worth
Wd 0 w88 14x Jiz 1041517 1 = and box of 3 5470,170 14 W 170 DVDs the worth worth 38 0 DVDb, box contains 1 systeonef 82 W worth...
5 answers
) Determine the remainder resulting from the division of (n4 3n} 2n? + 4) by (n + 2). Use the remainder theorem.
) Determine the remainder resulting from the division of (n4 3n} 2n? + 4) by (n + 2). Use the remainder theorem....
5 answers
Consider the following complex-valued function of real variable:x(t)2e(5-3i)tWhat are the real and imaginary parts? Fill them in below:x(t)What is the derivative? Fill in the real and imaginary parts. (You can take derivatives of the real and imaginary parts above, or you can compute x' (t) = 2(5 3i)e(s-3i) _ They should give the same answerl)x' (t)
Consider the following complex-valued function of real variable: x(t) 2e(5-3i)t What are the real and imaginary parts? Fill them in below: x(t) What is the derivative? Fill in the real and imaginary parts. (You can take derivatives of the real and imaginary parts above, or you can compute x' (t...
5 answers
(12 points) Zx for x and y in terms ofu and (a) Solve the system u =x+ Y,v =y - akxy2 (b) Find the value ofthe Jacobian u,v Vx+yly 2x)2dydx. Evaluate the integral J3 (c)
(12 points) Zx for x and y in terms ofu and (a) Solve the system u =x+ Y,v =y - akxy2 (b) Find the value ofthe Jacobian u,v Vx+yly 2x)2dydx. Evaluate the integral J3 (c)...
5 answers
Points) Consider the sequence{an}xzo = {2,7,12,17,22,_}i) Find the next two terms in the sequence.ii) Find a recurrence relation that generates the sequence, specifying the value of a0.iii) Is the sequence monotonic (that is is it increasing Or decreasing)?iv) Does the sequence converge Or diverge? Briefly explain why:
points) Consider the sequence {an}xzo = {2,7,12,17,22,_} i) Find the next two terms in the sequence. ii) Find a recurrence relation that generates the sequence, specifying the value of a0. iii) Is the sequence monotonic (that is is it increasing Or decreasing)? iv) Does the sequence converge Or dive...
5 answers
Let f(x) = kx?(1 and f(x) =0 if x <0 ~) ifo <x< Or * > L. (a) For what value of k is f a probability density function? (b) For that value of k, find P(x > h). (c) Find the mean.
Let f(x) = kx?(1 and f(x) =0 if x <0 ~) ifo <x< Or * > L. (a) For what value of k is f a probability density function? (b) For that value of k, find P(x > h). (c) Find the mean....
5 answers
The last snowstorm lasted 6 hours. Over that time, the amount of snowfall was measure hourly, except for at the Sth hour when Mr, Pearce watched the 3rd period of the Leaf gameCalculate _the correlation coefficient,T, using the given formula Time (Hours) Total Accumulation% EyExEx?ExyEyzUseful Formulas n(Exy) (Ex)(Ey)V[n(Ex2) = (Ex)]n(Ey2) = (Ey)j
The last snowstorm lasted 6 hours. Over that time, the amount of snowfall was measure hourly, except for at the Sth hour when Mr, Pearce watched the 3rd period of the Leaf game Calculate _the correlation coefficient,T, using the given formula Time (Hours) Total Accumulation % Ey Ex Ex? Exy Eyz Usefu...
5 answers
QUESTIONWhich of the following is an allowed set of quantum numbers (n, I, m, ms) for an electron in a multi-electron atom? n = 1,/= 0,m = Yz, ms = _ Yz n=2,/= 0,m= 1,ms = Yz n = 3,/= 2,m =-2,ms = %z n = 3,/= 2,m =-Y1, ms = 0 n = 3,/= 3,m =-2, ms = Yz
QUESTION Which of the following is an allowed set of quantum numbers (n, I, m, ms) for an electron in a multi-electron atom? n = 1,/= 0,m = Yz, ms = _ Yz n=2,/= 0,m= 1,ms = Yz n = 3,/= 2,m =-2,ms = %z n = 3,/= 2,m =-Y1, ms = 0 n = 3,/= 3,m =-2, ms = Yz...
5 answers
Population of beetles was scored for color The frequencies of the genotypes and their relative fitness values are given in the table below: Genotype BB Phenotype Black Brown White Frequency |0.16 0.48 10.36 Fitness 0.7 0.91What is the average fitness for color in this population of beetles? Please round your answer correctly to 4 decimal digits.Answer:
population of beetles was scored for color The frequencies of the genotypes and their relative fitness values are given in the table below: Genotype BB Phenotype Black Brown White Frequency |0.16 0.48 10.36 Fitness 0.7 0.91 What is the average fitness for color in this population of beetles? Please ...
5 answers
12.00 10.00 9 91.002.003,00 SB4005.006.00
12.00 10.00 9 9 1.00 2.00 3,00 SB 400 5.00 6.00...
5 answers
Quslon HelpDolenine Iho columnsMelaia Ho bncnily indopendent sclSeled Econed choice below and @ln the answer box complclochoicoThe cotumns 010 nol Iineanly =dcpondenl bocairg Lhe reducod row echalon Notn "0 ucolun nr Lcatty ndcpendenl bucause bic Icduced fow ochobn lorm 0' [ ^ 0 ]e
Quslon Help Dolenine Iho columns Melaia Ho bncnily indopendent scl Seled E coned choice below and @ln the answer box complclo choico The cotumns 010 nol Iineanly =dcpondenl bocairg Lhe reducod row echalon Notn " 0 u colun nr Lcatty ndcpendenl bucause bic Icduced fow ochobn lorm 0' [ ^ 0 ]e...
5 answers
Calculate (01 e25x'+4y dx dy, where D is the interior of the ellipse (3)? + (3)? < 1 (Use symbolic notation and fractions where needed )Il e25x'+4y dx dy
Calculate (01 e25x'+4y dx dy, where D is the interior of the ellipse (3)? + (3)? < 1 (Use symbolic notation and fractions where needed ) Il e25x'+4y dx dy...
5 answers
(-3 x10` -1)(-2x109)Write your answer in scientific notation.
(-3 x10` -1)(-2x109) Write your answer in scientific notation....
5 answers
Noidconstruct polynomial function that represents the required information. Use the wntten statereni Then the sides are folded up t0 make a open box Express Teet are cul oul Trom cuch comer rectangle [5 twlce as long as It I5 wideSquares wlth sides measuring where V Is measured In squar Teel. the volume Vof the box as function of the width
Noid construct polynomial function that represents the required information. Use the wntten statereni Then the sides are folded up t0 make a open box Express Teet are cul oul Trom cuch comer rectangle [5 twlce as long as It I5 wideSquares wlth sides measuring where V Is measured In squar Teel. the v...

-- 0.118734--