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Aldmiona 81 remalning bvunp auabuv Llii appropriate L Slawant 8 1 E V Try Again; indino Jlod V averade vour answel With te :122 JoJUI Vonw Submit Pan D 11 U 1 V 13 ...

Question

Aldmiona 81 remalning bvunp auabuv Llii appropriate L Slawant 8 1 E V Try Again; indino Jlod V averade vour answel With te :122 JoJUI Vonw Submit Pan D 11 U 1 V 13 1 U

aldmiona 8 1 remalning bvunp auabuv Llii appropriate L Slawant 8 1 E V Try Again; indino Jlod V averade vour answel With te :122 JoJUI Vonw Submit Pan D 1 1 U 1 V 13 1 U



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$\mathrm{K}_{2} \mathrm{CrO}_{1}$ givcs a ycllow precipitare on rcaction with: (a) $C_{4}^{2}$ (b) $\mathrm{Fe}^{3}$ (c) $\mathrm{Ba}^{2}$ (d) $\mathrm{Pb}^{2}$

They're. So for this exercise we have this vector B. And the subspace dovey generated by the one, V two and V three that are these vectors that are defined here. So basically we need to calculate the Earth a little projection of you on this space to view. And just remember remember this projection is calculated as the inner proud of the vector V. Each of the generators of this subspace dog. In this case the generators RV one, The two and 3. So we need to calculate the we need to calculate the inner part of me with each of the generator divided the score of the norm of the generators times degenerates. So these for the three vectors B two square plus the interpreter of B would be three. B three. Did the square of the norm of B. Three. Okay, so just to remind you a little bit of the geometric intuition of this, is that the view is generated by these three vectors. So what we're doing is projecting we on each of the generators and then some that together. So we want We t. v. one and V three acts as a basis. Actually in this case they are linearly independent so they form a basis for this. Yeah, subspace of you. So we're writing the in terms of this basis. So we're projecting projecting on this sub space. So let's calculate the correspondent values that we need. So in this case we would be one. The product of B would be to dinner product of the would be three. So this is equal two, one half, There is a constitute and this inner product is equal to zero and then the norms. So because this is the cost to zero means that we don't need this term anymore is going to be equal to zero. So we just need to calculate the score of the norms for B. two and B one. So for me, one square of the norm, remember that there is equal to the inner product of the vector with itself. And in this case this result in one and the inner approach of B two square is equal 2, 1 as well. So these are actually military vectors. And then we just need to put all together on the four. So behalf that the projection of the vector B on the subspace, our view, it's equals to 1/4 times 11 one plus the vector V two. That is equal to one, 1 -1 -1. After some. In these two vectors obtain the action solution that is one half times the vector, three, three minus one minus one. That corresponds to their thermal projection of beyond this subspace of you.

We need to refine the grain property. Let u equal to you. Want you to Onda be equal to be one. Me too Now consider the left on site. So substituting their abuse we get We won me to bless Do one you do minus the one may do so let us simplify the dorms Insect ban Emphasis So it this you want minus? We won. Come on, You do minus veto. No, no, This ad needs to reckless over this. Everyone bless you Want minus me one? Come on, They don't unless you do minus veto. Now you can cancel out the common terms with different signs. So they get you want Mama, you do. This is nothing but the victor. You hence the property is very fight.

Hello, everyone. So we have been given three factors. You v n w Okay, in their component forms. Okay. And we have to verify these troops These two expressions which are actually property number seven and eight from the boss in Ways Number 86 83. OK, so the 1st 1 uh, will be let us started it. So I will start with the left hand side. So that is a B which isn't bracket. Then we have the factor, V Okay, so we have to ah, come to the right in sight, OK, after evaluating. So let us start So a b r scullers. So we put it here, and v is a vector. And its component form is V one comma veto. So we're gonna write it like this. Okay, fine. So we can, um, eliminate the record and write the whole expressionists E b few one comma V. Okay, so actually a beer scaler. So the product of a B would also be a scaler. So it be the birth of baby Jesus, escalate. Okay, so this Keller can be multiplied with the component form. We won't envy too. No, we can Group B and B one b two. Okay, Because their skill er's it is absolutely fine. Group this. Okay? No. Ah, change in the value local. Okay, so that means we have a then B and the complaint form is we're gon come a V two. So in the vector, that would be vector V. So we're here on the second part. That is the right inside. Okay, so we have very fight this one. Okay, so now we will come to the next question which is one multiplied vector vehicles to vector V. Okay, so this is the most easiest one. So one are deployed with factor v can be glutinous. One multiplied with its components. Sorry. Computers do not have vector saying they're scallops. So v one comma V two. Okay, so we know in the scaler Here it is. Won can be multiplied individually with the individual components. Okay. So we can multiply one with the one as well as for you two. So that is one multiplied with everyone comma, one multiplied with free to. Okay, so here that is one multiplier. Everyone is. Everyone on one multiplied with me to his veto. Okay, fine. So we can write this component form into the vector from which is Vector V. So we have also verified our second expiration. So one vector V equals to victory. I hope you have understood. Thank you.

And this problem we are given that Matrix A. is the three x 2. Matrix six I get 1- zero. Now you have 34. Mhm. And Matrix B is the Matrix Uh huh. 31 And yet 1560. And we want to find first A plus B. Now to add to major cities, you just add the corresponding components together. So top left close, Top left Is what goes on. The top left search plus three is 9. Top ride was top ride, It was in the top right now give one postponement 0. And then we proceed in this matter. Two plus negative one is one, zero Plus 5 is five. They have three plus six is three Than 4.0. As for And so that is our Matrix A plus B. Now for the Matrix A minus B. Take our correspondent components again and subtract the light terms 6 -3 is three -1 -1 is -2. Two minus negative one is three, 0 -5 is -5. Then you have 3 -6 is -9. 4 0 is four. Now for two a. We take everything and a and multiply it by two. six times 2 is 12 in one times two is that you have to We have 40 -6 and eight. And then lastly we want the matrix negative three C. I'm sorry, 93 B. Three B. That means take everything and be and multiply it by negative three 789 Now you have three. Three may have 15 negative 18 zero.


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