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Rrals 21 the U 1 1 1 11 ino Save8He...

Question

Rrals 21 the U 1 1 1 11 ino Save8He

rrals 2 1 the U 1 1 1 1 1 ino Save 8 He



Answers

$\mathbf{u}_{1}=(1,-3), \quad \mathbf{u}_{2}=(2,2) \quad$ 28. $\mathbf{u}_{1}=(1,0), \quad \mathbf{u}_{2}=(3,-5)$

This video's gonna go through the answer to question number 11 from chapter 9.3. So ask to use real reduction to find the inverse off the matrix. That 11 one 121 Thio three. So So we conform the combination matrix with the identity and they tried refugees. Okay, so if we subtract to you off the top equation from the bomb equation, then we're gonna get zero one that to you, minus 20 Maybe it's gonna be minus 201 on the inside. And if we should bottle subtract one of the first question from the middle equation, that's gonna be zero That's gonna be one on that's going to zero months. Well, on zero on me, the top equation as it is, Savior zero. Okay, so now we get to be a stick in court because on left inside the bomb equation on the middle or after the bottom row of the majors in the middle of the matrix. All the same, which means that the ah, the row is off the matrix linearly dependence, which by their a born in the book, means that er the identity that's all right with me

We're given this magic A We're universe first. Me from the convertible meeting room. Without it, the determinant they You could have zero in a but not in veritable works. Check it. A convertible. What do you say? Actually, I read it down here. Let's find a determining a check of the convertible or not. 111 First, I'm gonna high road to buy world one by negative one and had it wrote to So I guess one might one minus one zero. Making one plus 21 No one here. Next I'm gonna multiply growth three by negative one times wrote to I get 111 negative. Q one is negative one. You know, the determining the mortification old the numbers in the pivot in the diagonal interment is clearly not so. Therefore, we can find a neighbor nullifying chambers through the over inside the right chambers on this side. Very eight in the side. You're a here you have the identity matrix for three by three One here is you here alone? Now we're gonna really do until this side here. It looks like this. Once we do that, we will get a members on this side Look for reduced. Well, we already thought before we're finding the determinant. Do it again. First they can about this here. 11 now weaken Can't hold this position here. Negative one. They won negative times. Negative. 101 Negative. 101 Here one. Now weaken. We can scale the throw here. We can divide the group by negative one. We get negative here. Also here. Positive here. Now I can scale road three by minus a few. Added row to cancel this The negative too. Times road Here. That positive you minus one. That's one. Make a few plus one minus one. Two zeros too. You get one Next. We just need get rid of this. We can. He gave the period. Rowing added to the first would be a bit of this one. Here. You never get here from zero and in one one to negative one plus 01 and 101 Now you get a second road out of the first road in negative. One plus two. Just one. You have one plus minus +10 You have minus to plus one. You hear? This is the identity matrix implies on this side. He had a members say in verse, should be one bureau minus one one, minus 12 and minus 11 minus 11

We have a lot number 16 and this uh metrics is big and being given a call to 2 -1, 1- went to -1, 1 -1 and two. And we need to verify that. A pew -6 years choir plus nine eight minus for a zero and then find a English. Okay so for that we have to find first is where then a two a square is A into a. So let us write the mattresses 2 -1 1 -1 to -1 1 -12 into same same thing. Two miles 11 miles 12 -11- went in to Okay so it will be two into two for Plus one because we are multiplying like this to place when that's where For a pleasant person and -2 -2 -1 then two plus 1 plus two And then -2 -2 -1 one plus four plus one -1 -2 -2, two plus one plus two and minus one minus two and minus two. One plus one. Place for. So a square becomes equal to six minus five. Five minus five And six and -5. This is five miles 5 and six. Okay so a cube is a square into a A square into a. So a square is 6 -55 and then -56 -5. five miles 5 six and 2. It is 2 -1. 1 -1 to -1 1 -12. This is six into 2 12 A plus five plus five -6 plus 10. We are multiplying like this -6 plus 10. So in -10 my understand And then -5 six plus five. Last 10 -10 -6 minus five. Then five place 12 plus five And then -5 -6 -10. 10 plus five. That's six -5 -10 minus six. Five plus five plus 12. Okay so A Q. Becomes equal to 20 to -21. minus 21 22 and -21 K. 21 -21 and 22. This is a cube now we will be playing in the question. The question given is AQ -6 A square six years squared. Mhm. Last nine A minus for a. So let's stop the equation is this let us start liking the values 22 -21 21 -21 22 minus 21. 21 -21 22 -6 Esquire Esquire has the value mhm Six -5 and five -5. -5. 5 -5 and six plus nine. He has the value given value to -1, 1 -1 to -1 And 1 -1 and two. And then minds for a the minus four, 1000 1000 and one. Okay so this will be equal to right? 22 plus 36 plus 18. Because the 22 plus six we multiplied with is the age of the member. So 36 Plus 18 Plus four. Okay so this comes out to be 22 plus 36. 22 plus 36 plus 18 minus equation minus six X squared minus six square. Well the equation so it should be minus And then -4 so it should be minus two. Okay so 22 -36 -36 plus 18. Mindful This is -21 plus 30 blessed today minus nine. It will be zero thurday's 21 -30. 21 -30 Uh plus 9 0, Last 9 0. So here the 2nd row it will be -21 -21 plus 30 Plus 30 and plus 18 plus 18. Okay -10 to plus Turkey. My name's -9-0. Then 2nd is 22. Mine statistics 22 minus 36 plus 18, nine and two. So 90 to 18, 22 mile statistics matters 18. And mine is poor. And this uh -21 place that there -21 was 30 minus night at 10:30. minus 30. 21 -30 plus nine. Thank you. Very minus 30. Bless mine. Yes. Second is This -21. Last 30 -21 plus 30 -9 and 30 days. 22- Statistics 22. My statistics Plus 18 -4. So brah 000000 and 00 and zero. Which is equal to oh our artists has been proved okay now we have to find a universe. So let us multiply given the question Which is a Q -6. Are you square 36 years prior? Six A Squire. Last nine A minus for a. Oh okay. Let us take the equation. A cube success where 9 8 miles for it. Okay so this will become yes but a minus six. Ai bless mine. I minus four In verse A. The N. Was A. And simply dangerous equal to O. Mhm. Now for a universe will be equal to six a. Because a. Is always a six A minus a Squire plus nine A. So six a. means we have six. Hey Brenda is two months 1 one 2 -1 and one -1: -1. 1 -12. This is a minus is but it's quite has Value 6 -5, 5 -5, -5 5956. This is for his question. This value And what else? Plus mine. I So plus nine. I asked the identity matrix of order three x 3 1000 1000 and one. So if we add it will become 12 six plus nine minus six plus five Bleh zero and 6 minus five brazil oh minus six plus five. Black, zero 12 -6 plus nine and minus six Plus Fire Brah zero six minus five brah zero minus six plus five plus zero 12 mine six plus nine. Good. So this comes out to me doing minus 50. Okay nine plus 6 15. This is 12 mm 16. Okay so this is uh this will become equal to for a square equal to a square it should have been placed and it should have been minus And it should have been -2. No, it is blessed. No problem. So there should be plus, They should be minus. So they should have been minus place place and this is minus, this is minus this place. This place, this is minus this uh minus this place. This place they should be minus minus plus. Bless, Okay, they should be minus minus and plus. So There should be three one -1, 1, 3, 1 -1, 1 and three. And this is four and verse. So if you need to find a universe we have to just divide by for like this. So this is the value for a diverse

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.


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