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3 4u V6 !xc"` [ =< x=y-1 1 !'1' ' 1} AOi x=Vy4 X...

Question

3 4u V6 !xc"` [ =< x=y-1 1 !'1' ' 1} AOi x=Vy4 X

3 4u V6 !xc"` [ =< x=y-1 1 !'1' ' 1} AOi x=Vy 4 X



Answers

$$ \begin{array}{|c|cccc|}\hline x & {3} & {6} & {9} & {1} \\ \hline P(x) & {0.3} & {0.4} & {0.3} & {0.1} \\ \hline\end{array} $$

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

Hello students. So in this question we have to determine one program per meter cube. It is equal to what? Okay so we have to convert these units because uh in the question in the options we have Graham or centimeter cube units. Okay so we will convert these units. So one program or meter cube. This can be written as this. Okay, so Desert is one and one program from the conversion table using one program this is equal to 1000 g and one m. It is equals 200 centimeters. Okay so substituting these conversing values here. So we will get that one more player by one program which is this 1000 g. They were by one m which is 100 centimeters 100 centimeters. And this cube. Okay so from here after solving we will get that we will get that. This value will be one by 1000 gram per centimeter cube. Okay so from the given options options second it is the correct answer for this problem. Okay so this becomes the answer for the given problem. Okay thank 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.

Okay, so this problem wants me to solve the equation. One over X minus two minus three X over X minus one is equal to two X plus one over X squared minus three X plus two. The first thing I notice is that this quadratic has factors of X minus one and X minus two so we can easily get all three of our denominators to be the same. So I'm gonna multiply my X minus one term by X minus two over X minus two and my X minus one term by X minus line, and then we'll have all common denominators. Also, I know because of that that when we're checking for extraneous solutions at the end, ex cannot equal of one or two is that would leave a zero in the denominator, which is not part of a domain of division with polynomial. Okay, So, multiplying by those I'm gonna have, uh, we just need to solve my new writer at this point, so we're gonna have X minus one minus three X square plus three X. That's just distributing the three XX minus two distress expense too. So, uh, three x times negative two is Ah, positive. Six Xnegative three extends Negative, too negative. Three X times access Negative three X squared and one times X minus one is okay. Every day it's over to solving for when that's equal to two X plus one. This is going critical. Andranik. So we're going Teoh, Let's move everything to the right. Science. I have a positive X squared term. So we're gonna have zero equals three X square, round two X minus six X minus X Should be negative. Five acts and then we're gonna have one plus one. So plus two, case of this factors to zero me close. I was trying his three x minus two times X minus one. There's really only two options that this could be If it factors, I'm just checking this to see if it works. So three X minus two times expense while about three x squared Negative three x five acts. Yep. Unaware you get used to doing these and you just start seeing the patterns because my leading coefficient was a three. If it factored, that meant like either one of my factors had to have a three on the front so and then to only has one into its factors, So there's really only two options to go through. It could have been three X minus one and X minus two. That would that would have been my second guess. Anyway, because of the zero property X has to equal 2/3 or one. But if you remember from the beginning, ex cannot equal one or two. So one is an extraneous solution. So our only viable solutions that X is equal to 2/3. Okay, thank you very much.


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