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M B 1 i 1 1 1 W 1 il 1 9 V 8 8 J : 1 V H K J! 8 L 8 3 3 ill...

Question

M B 1 i 1 1 1 W 1 il 1 9 V 8 8 J : 1 V H K J! 8 L 8 3 3 ill

M B 1 i 1 1 1 W 1 il 1 9 V 8 8 J : 1 V H K J! 8 L 8 3 3 ill



Answers

$\begin{array}{|c|c|c|c|}\hline m_{i} & {8} & {1} & {4} \\ \hline\left(x_{i}, y_{i}\right) & {(-3,-1)} & {(0,0)} & {(-1,2)} \\ \hline\end{array}$

In the problem we have 56. And this is yeah it is gen X get works. Get three X. Get your necks. It's two weeks is tricks plus if one X after works three X gen X G networks. GTX H one X. HdX history X plus. If you're next afterwards after the X. And the one x. Networks G three X H one X H two x. and three x. No further. We have fds a. And this equals two. If one yeah. Have to wear after a year. Do you want to G two A. Gayatri? H one A. It's too good. Is three. Okay. And these are reputed To two times more studies if one A. Have to A F three given a and geeta, Geeta A 20 H two A. It was today glass if one after where have today do you want to? They were the tree H one A H two A is three. Now this equals to zero plus zero plus zero which is equal to zero. Since F R A Is equal to zero. G R A is equal to H R A. Is I mean this equals to 04. All the times that is if R0 gr hr is also zero For Article 1, 2 and three. So we have this as the answer to the problem

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.

K two Cr awful gives a yellow precipitated it's a yellow policy heated on reaction with on reaction with Be a two plus, as well as B B two plus, therefore, option C and option the uh, correct answer for this problem, Option C and option B. R. Correct answer for this problem.

In this problem we are going to use the properties of mattresses and they're in verses in order to simplify a given mattress expression. Now the given matrix expression is E C inverse whole inverse times E C inverse times E C inverse whole inverse times E. The envious Now in the question it is said that a B C and D. Are all in vertebral mattresses. Now let us begin to simplify this expression. Now, first of all, what we have is easy inverse inverse times, easy inverse. That means that the matrix easy inverse has its inverse multiplied with this original matrix. Now, since the product of any metrics with its inverse is equals identity matrix. Hence a C inverse inverse times a C. In verse will be the identity matrix. I. With this we multiply the remaining two terms A C inverse inverse times a. D. In verse. Since any matrix multiplied with the identity matrix, is that mattress itself? This will be equals to A C. Involves inverse times A. D. In Vegas. Now using the property of matrix inverse, which says that a B hole in verses equals to be inverse. The inverse E C inverse hole in verse will be equals to see inverse inverse times a inverse. And with this we multiply a. D. Universe which are the last two terms of that expression. Now see inverse inverse will be equals to see because the inverse of any inverse is the original matrix itself. Next we have inverse. E be endless. Now, since matrix multiplication is associating, we can group together the terms however we want without changing the order. So let us group together to terms a university. And then we use the property that the product of any matrix inverse is equal to the identity matrix. So inverse A. Will be equal to I. And we are left with C I. D. In most now since the product of any matrix of the identity matrix is the matrix itself and ci is equals to see. And with that we have at the end the in laws, so that means that our metrics expression is simplified to CB in Vals.


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