5

(1.5 Mar_ ks) Prove that for Any vectors (, b And c in a vector space VSpan{a,b,e} = Span{a - 6,6 +C,c}...

Question

(1.5 Mar_ ks) Prove that for Any vectors (, b And c in a vector space VSpan{a,b,e} = Span{a - 6,6 +C,c}

(1.5 Mar_ ks) Prove that for Any vectors (, b And c in a vector space V Span{a,b,e} = Span{a - 6,6 +C,c}



Answers

Prove: For any vectors $u, v \in \mathbf{C}^{n}$ and any scalar $z \in \mathbf{C},$ (i) $u \cdot v=\overline{v \cdot u},$ (ii) $(z u) \cdot v=z(u \cdot v)$ (iii) $u \cdot(z v)=\bar{z}(u \cdot v)$.

Hi. So for this exercise we have we need to consider to be actors, you and be and you and these two vectors satisfied the property that for any other vector W. Let me regret this better for any other vector W. Did that product of you with W is equal to the product of B. W. Okay. If this is satisfied for every vector W, then that implies that you is equals to be. We need to prove this statement. This called cancellation law. Okay, so let's take let's big a generic vector W. Okay. So any any any any vector. Okay. It's an arbitrary vector such that you The product W is supposed to be that product. Okay. We can see that we can regret this as you the product of u minus V. The product of U equals to zero. And we can regret this as U minus V. Dot product W equals to zero. So here it can happen to things. Either W is perpendicular to each of these vectors or u minus B. R is equal to zero. We considered a generic vector dollar, so it is not true that this vector is perpendicular to these two. It's not necessarily true that this W here is perpendicular to these two vectors. So we are considered a generic case. We pick a generic vector dog, so this is not true generically. So the only thing that we need to consider is that u minus V is equal to zero, and this is equivalent to say that U is equal to be.

Yeah. Okay. We're going to show that if a Scaler in Visa vector than the magnitude of a V equals the absolute value of a times the magnitude of V. So how are we going to do that? Well, we're going to come up with our vector V. And I'm going to call it V. Of X in the I direction plus V. Of Y in the J. Direction. And then I'm gonna actually multiply that Scaler a into my vector. And I know that when I do that I multiply it into each of my components. So now if I'm going to find my magnitude, I will have a a times V. X all squared plus in a times B Y all squared. To clean this up. I can square each one of them separately. The next thing because there is an A squared in both my terms, I can factor it out front and then I can take the square root of a squared. Well whether a started positive or negative, if you're going to square it and then take it square root, it does end up positive. So we can add that absolute value of A. On that. And you can see how now this looks like the absolute value of a, multiplied by the magnitude of the vector V.

Any given question. We have three vectors you b and w. So we have to prove the four leading property call you Plus. Then they don't w seven The equal go you don't conduct. Yes, the dog Associative property director Reason. So we have to do through this. So you started as young that uses Vector one. Call you one. He's in the vector a do be to and go through meter a tree Cuomo Petri But when the left hand side of the property plus the dark on dark blue is a acquittal, so you bless you will be a one calma p. One. Thus the ISS A to comma b two. No productive a tree on the tree. Now this is acquittal a one that's a two coma. Be one. Let's be true. No productive a tree common Vetri. So when it from the daughter person, we will get Hey, one rescued toe. That's market. A tree. Yes, the one that's beautiful sprinted the three. So when we do this, we get a one it to us A. To a tree plus B one B three plus B two b tree solving the right hand side of a Christian. We get you, Doc. That blew us the dark. So this is equitable. A one Coleman. Be one I put up with a tree tree. Those he go, a tree gonna be a tree. So when this is simply fired, we get you won. Here. Three This the one to be three less a do. Hey, three. That's the do the she when we compare the Expressen number one an expression number two We get to see that they both have seen Tom's. It is He won a three. He won a tree That's you to a tree. That's a poetry b one b three this be one Petri, and we will be true. That's you to get you. So therefore we have groups successfully. There you less be Then dark blue re care you don't do this is equally you have Lupus. I mean, thank you

So in this question we have a scaler. He Victor, you earned another victory. But we haven't asked to prove this for Lingard Entity that this here you dork will be a sequel. Yeah, Dog into you. Dark equivocal. You busy working, you dog? It will be to prove this identity. Who knew that? There as you That you you won o b one. That is the question. Now here. By substitution, we'll find the most if you don't be so. This is equal here. Here's one call. Must be one Dr. They do Mambi. So this is a quartile. Here is one. Mom. Mom, You B one dark A to coma. This is a quote. If they're simplify this, you get They're not here. Here. One here too. That's B one. And this will be a cordial here. Have been taken common. We get here one. Yes, the one beating. So there's a probably we get and this is a scaler. Quantity similarly will proceed with the second bomb. This so solving the second round. Pick it here. You dark the so in position you get here are just a bit. Here's one Well, one You who quantity do So business. Peak organ here is one year too. That's B one. This is a very we get from storm. So don't three you have you? No. Hey, is this Gordon? You iss here I will be your wife. We have got it. You were will be since this week it were you go here. Well, you said you Goemon opening the door cooperation He kept you one here. That's B one here People taking Kikkoman upside We're left with a one a two That's the one people comparing the expressinstall grain by solving one you and treat you get seeing their lives here. This is a murder Even I could just Young people here are the perfect here whenever we want equal a market Pretty when I took this So therefore one is a cortical. Who? The sequel. Good three. This in place here You dark Be mystic Burton. Here you go. You see? Go, you dog theory. So we have, uh I didn't get to hear


Similar Solved Questions

5 answers
Let X and Y be two topological spaces. Prove that f :X +Y is cOntinuous if and only if f-'(C) is closed for each closed set € cY,
Let X and Y be two topological spaces. Prove that f :X +Y is cOntinuous if and only if f-'(C) is closed for each closed set € cY,...
5 answers
The profit for a company is P = 10Ore- %/400 wherethe production level_ Use differentials to approximate the change in profit as production increases from 120 to 140.
The profit for a company is P = 10Ore- %/400 where the production level_ Use differentials to approximate the change in profit as production increases from 120 to 140....
5 answers
[-/1 Points]DETAILSSESSCALC2 6.3.028. 0/20 Submissions UsedMY NOTESASK YOUR TEACHERPRACTICE ANOTHEREvaluate the integral:x2 + 4x + 13g( tAm Need Help? Rahetm(Ahl -'(2)aeanaia
[-/1 Points] DETAILS SESSCALC2 6.3.028. 0/20 Submissions Used MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the integral: x2 + 4x + 13 g( tAm Need Help? Rahetm (Ahl -'(2) aeanaia...
5 answers
More Examples Predict molecular polarity of XeF4 XeF:Cl XeFzClz
More Examples Predict molecular polarity of XeF4 XeF:Cl XeFzClz...
5 answers
Write up the fourierseries forthe function flx) with period T=2tf(x) =Ixl for TsX<Twhat is a3?9 4t04 91419T
write up the fourierseries forthe function flx) with period T=2t f(x) =Ixl for TsX<T what is a3? 9 4t 0 4 91 41 9T...
5 answers
Use the price-demand equation below to find E(p) , the elasticity of demand X= f(p) =25,000 65OpE(p)
Use the price-demand equation below to find E(p) , the elasticity of demand X= f(p) =25,000 65Op E(p)...
4 answers
Water is oxidized to oxygen by:(a) $mathrm{H}_{2} mathrm{O}_{2}$(b) Fluorine(c) $mathrm{ClO}_{2}$(d) $mathrm{KMnO}_{4}$(e) Ozone
Water is oxidized to oxygen by: (a) $mathrm{H}_{2} mathrm{O}_{2}$ (b) Fluorine (c) $mathrm{ClO}_{2}$ (d) $mathrm{KMnO}_{4}$ (e) Ozone...
5 answers
What is the difference between a DNA virus and a retrovirus? ( $21.9)$
What is the difference between a DNA virus and a retrovirus? ( $21.9)$...
5 answers
A Find derivatives:1.Kx) = 2. 2+I2 flx)2) 4.Kx) = 43.fr) = (x+ 1)S(? +x)'
A Find derivatives: 1.Kx) = 2. 2+I 2 flx) 2) 4.Kx) = 4 3.fr) = (x+ 1)S(? +x)'...
5 answers
(8)+() + + (4)=? n is odd
(8)+() + + (4)=? n is odd...
4 answers
Two parallel metal plates of area 2.04x10 : m? and separation 8.27x10-` m have an electrie field in the region between the plates of 5.80*105 Vlm: What is the electric potential difference between the two plates? How much energy density due to the electric field in the region between the plates?
Two parallel metal plates of area 2.04x10 : m? and separation 8.27x10-` m have an electrie field in the region between the plates of 5.80*105 Vlm: What is the electric potential difference between the two plates? How much energy density due to the electric field in the region between the plates?...
5 answers
How do index fossils aid correlation?
How do index fossils aid correlation?...
1 answers
Match each function with its calculator graph. $$y=\cos 3 x$$ (GRAPH CANNOT COPY).
Match each function with its calculator graph. $$y=\cos 3 x$$ (GRAPH CANNOT COPY)....
5 answers
Civen tnat ccno was not involved_ what proportion oftne accidents were single venicle? 50/75 Or 66.6791 50/170 or 29.4190 25/75 or 33.338 25/230 or 10.8710
Civen tnat ccno was not involved_ what proportion oftne accidents were single venicle? 50/75 Or 66.6791 50/170 or 29.4190 25/75 or 33.338 25/230 or 10.8710...
5 answers
(3x+l)"+1 Wnat is tne interval of convergence ofthe series En=1 2n +23 sx<03 Sx<03 <x<03 <Xs0
(3x+l)"+1 Wnat is tne interval of convergence ofthe series En=1 2n +2 3 sx<0 3 Sx<0 3 <x<0 3 <Xs0...
5 answers
Mean, mode, standard deviation, and range are forms analysis used to describe the sample dataset in such way 35 to portray the "typical" respondent and ta reveal the general pattern of responses_ difference inference descriptive association
Mean, mode, standard deviation, and range are forms analysis used to describe the sample dataset in such way 35 to portray the "typical" respondent and ta reveal the general pattern of responses_ difference inference descriptive association...
5 answers
EctQuestion 40 / '10 pts2.5 grams of copper (IIl) nitrate reacts with 3 grams of Magnesium hydroxide What is the limiting reactant?
ect Question 4 0 / '10 pts 2.5 grams of copper (IIl) nitrate reacts with 3 grams of Magnesium hydroxide What is the limiting reactant?...

-- 0.031425--