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2 2 7 1 Il ; 3 [ V { 1 ibl ! 2 1 HL 3 HL 1 [ [...

Question

2 2 7 1 Il ; 3 [ V { 1 ibl ! 2 1 HL 3 HL 1 [ [

2 2 7 1 Il ; 3 [ V { 1 ibl ! 2 1 HL 3 HL 1 [ [



Answers

$\left[ \begin{array}{lll}{1} & {1} & {1} \\ {1} & {2} & {1} \\ {2} & {3} & {2}\end{array}\right]$

This video, We're gonna go to the answer. A question of a 13 from Chapter nine White three for us to find the inverse off. The matrix minus two minus one 210 31 minus four. So let's combine this with the identity matrix once there is, There is there were once they were serious, they were What? Yeah. Reduce. So that's that three altitude of the first row to the bottom room. So that's going to go to zero. Ah, mine is 1/2 minus one ad for you, too, is 1/2. I want us to be over twos to you too. Keep a zero and one. And let's also add one of the first road to the second round. Get rid of this too. We're all scared of this wall. Uh, this becomes a wall 10 Top row stays the same minds to you. Minus one. Ah, whoa! 100 Next up, less subtract one of the middle row from Sapporo. So that's gonna be minus two minus one zero. Uh zero minus one zero. Minimo stays the same. 0011 What? Zero. That's also most black bottom are about to but zero minus 11 302 Next up, let's subtract one of the middle row from the bomber. That's gonna be zero minus one. That's zero at three months. Ones, too. They're minus one minus. Y T minus zero is too. Keep the middle. Where was it? Is seriously, Rabban. War hero. And keep the top roses minus two minus one. They were. They were minus one zero. Okay, let's subtract one of the bottom row from the top room. So I'll get rid of this month's one at zero minus two is minus two minus one minus 110 Uh, zero minus two is much too, kid made about the same there. Is there a woman? Rome on zero on dhe bomber. We can multiply by one, get zero. What? Zero. So most by my minus 1010 too, because minus two minus one equals one. T because minus two. Now, what we can do is most by the top row by minus, huh? It's gonna be born zero zero. Whoa, zero. What? Now you'll see that the form two rows. Uh, if we just flip these around, which you can do it, bro. production on. Then we get the I don't see a downside. So 010 That's what was the bottom room minus 21 minus two in the middle ground, which is not about tomorrow. 001 Well, zero on Dhe. This matrix here is the inverse off the matrix that we started with.

To find these two matrices together. Here. First thing we need to do is check the dimensions will work. Okay? First matrix we've got is two rows three columns. That's a two by three. The second matrix is a three row one column matrix. These inner two dimensions have to match which they do. That means is a resulting matrix will be dimension the outer dimensions. Okay, So we're gonna have to buy one. Matrix is our answer just two spots here. Okay, we'll fill in the first spot. This is gonna be row one. Column one. Okay, so everything in row one thinks everything in column one negative one times six plus zero times negative four plus seven. Thanks one. Okay, this should give us negative six plus zero plus seven. That should give us a one in that first little spot right there. Okay, The second guy this is gonna be row two column one. Okay, so we're gonna take everything in row two times that same column right there. So three times six less negative five that was negative for plus two times one spent 18 plus 20 plus two should give us 40. Okay? So one in the first row, 40 in the second round, and that is the result of this modification.

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.

Okay. We call about major modification here. When doing major modification. We want to do the rows of the first college by the time the Rose the first matrix by the column of the second matrix for each respective positions. So, for example, if it was the first row, first column is the first broken, the first color. If it was the first for a second column, if you first were against a second, call him. So that's what he's out here with. You first were against one out of three, and we get three. Top minus one by to say, three minus two is just one. Still, there are first rate second column here. You've got Mom minus two of the three tons. Three cells going minus. Tick on. Then you've got two times. One set. First right. Second column, say a plus to say this is gonna come out zero. Okay, Right now you've got the second. What have we got here? We're gonna go if you get a second race. There's column. Yeah. So you've got three launched. The one minus three minus 33 lakhs minus one equals zero. So zero here on, then you've got secondary second column minus two. I have three types. Er to over three. XB minus two or three times won't pastorate. So we actually with identity here s so these two should be actually in verses off each other. What you'll probably find is the determinant is, um 1/3. Yeah, it's 1/3. So all of these divide by three. And then when we do our in verses, you switch these around, which does not do anything on your time to use by minus one, so yeah.


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