5

8 1 0 0 } 5 5 1 F 1tii li V Jt { 1 0 3 0...

Question

8 1 0 0 } 5 5 1 F 1tii li V Jt { 1 0 3 0

8 1 0 0 } 5 5 1 F 1tii li V Jt { 1 0 3 0



Answers

$$\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & \frac{1}{2} & 0 \end{array}\right],\left[\begin{array}{ll} 1 & 0 \\ 0 & 2 \\ 3 & 4 \end{array}\right]$$

That's that's one for you with this one. Remember? Our are very so this one doesn't have any solution because we have our last Oh, it was us isn't true. Statement, so we can see that. Is this Listen, but right or all right. What are the right reasons so Or money? Sports. Why you gotta wait a solution? We thought so. This is more only work. Not all right.

In this video, we're gonna go through the answer to question number seven from chapter 9.5 West to find the argon values nine vectors off the matrix A given here. First. Do that. We need to find the determinant off the matrix. A minus. I ascetic with syrup. So this is the determinant. Off one minus R zero zero two three minus. Ah, one 0 to 4 months are You're wasting your over the top road Got one minus r times by the deterrent box Right to Buddy Matrix, which is remind us ah times by four minus R minus two. This is gonna be a one minus ah times by Ask what minus for our minus three hours. Minus seven are plus 12 minus to which is plus 10. Good. Then we can characterize this with one minus R and it's gonna factor Rise to be Ah. Minus five, uh, minus two. So we said that equal to zero. Then solve we're gonna have I can Values are is equal to one. I was equal to two on our secret five. There are three aiken values. Find their associates. I connect this starting first with I come back to rise. Because of what? When it's find the matrix a minus one times high times, the fact that you want is equal zero up. This is just 000 Good two to you. One on zero two three touched by yuan is equal to zero safe. Let's complete this by hand. So if you want, let's let the components be ex wives that then from the second World, we've got that to x close Thio. Why course Zed is equal to zero on from the third room we've got there, too. And two, Why close? Three is equal to zero. Okay, so this his bottom equation tells us that, uh, why is equal to minus three over two times that on the top equation tells us that thanks is equal to minus that minus half that minus why that's minus half said, plus three up to said. That's just ones that so, So X equals said, Let's just let them be ones. And that why's it was minus three or two time times said, which is just three. Everything. That's a first I Greta, the 2nd 1 we calculate with a minus, the less I connect it was too. Okay. Months to I times you want you could see. Right. That's gonna be a minus. 100 two 11 zero two four months. Two is two tells about you want zero? So the first hotels is not the first component. If you want equal to zero, then the bond to Rose. Tell us that Thea, the second and third components are next to each other. So if the 2nd 1 is one that the books reminds one, let's find the third Aiken Vector. Yeah, I can. Value was five comes I times you What do you want? It was there. So therefore months 400 two minus 21 02 minus one you want you see what Zephyr therefore you want? Well, the first component cto read off. That's just gonna be zero then. Second and for components are gonna be Will be, uh, yeah, we can tell from the second or the third World that if the second component is one, then the third component is twice second bone in, which is just too. That's a final act of Beckett

In this question we have to use row reduction to find the inverse is of the given batteries if they exist. And check it by multiplication. No, let us consider the metrics. Yeah. 123, 4 01, 2, 3 0012 0001. And on the right side identity metrics. Or for the four 1000 0100 0010 0001. Now we will row reduce the all metrics. We will apply the operation are funny those two our than minus two. Our two stores too, uh minus Artie And our three stores too. Our 3 -R4. On applying these operations, we get the metrics 1111. Yeah 01 11 00 11 little little 01. And on the right hand side we get 1 -10 needle 01 minus one deedle needle needle one minus one 0001. Again. We will apply the operation are one stores too, Urban -R2. Our two stores too, Our 2- Artery. And our three stores too. Our three minus are full on applying these operations to get the metrics 1000 0100 0010 0001. And on the right hand side one minus two, one needle 0 1 -2, one digital hell one minus two 0001. So in investment taxes, one minus two, one hero 01 minus 21 001 -2 0001. Yeah. Now we will check it by multiplication. We will multiply A. And N. Was matrix. So we can write a Multiplied by a invest metrics equals two 1234 0123 beetle beetle 12 0001. Multiplied by in west metrics 1 -210 0 1 -2 one. You know the middle one by understood deedle deedle? They're all one. No. Yeah all multiplication. We will first multiplied by stroke with first column. So one multiplied by one plus two multiplied by zero Plus three multiplied by zero Plus four, multiplied by zero On simplifying it we get one similarly. Now we will multiply first row by second column one multiplied by -2 plus two, multiplied by one, three multiplied by zero Plus four, multiplied by zero and simplifying it. Be good feel Now we will write these values in the desire my tricks, €1. By following a similar method we will find the other elements of the metrics. So you know beetle 0100 0010 0001. Hence hey multiplied by and was metrics. It were to identity matrix. Thank you

So this problem are given to functions F. And G. And they are related by the equation negative G of X equals negative F of X plus two. And were asked to use the numerical representation of F. Which were given to make a numerical representation of G. So here I put up top the numerical representation of F. Which were given. And we also have the X. Values that are relevant. And so at the bottom we're going to fill in H value of G fx based on these values. So start at X equals negative six. We have G F negative six equals negative F. Of negative six plus two. So negative six plus two is negative four. So F of negative four is five and negative F of negative four is negative five. Them. Okay now at X equals negative four. We have G of negative four equals negative F of negative four plus two. So negative four plus two is negative two. So F of negative two is equal to eight. And then we have negative eight. Okay, now at X equals negative two. We have G of negative two equals negative F of negative two plus two. Or f zero. So F zero equals 10. And then negative of that is negative 10. Now at X equals zero. We have G zero equals negative F of zero plus two or negative F of two. So F F two equals eight. So negative F F two equals negative eight. Now at X equals two. We have G F two equals negative F of two plus two or negative Ff four. Well, F F four equals five. So negative F of four equals negative five. And now at X equals four we have G F four equals negative F of four plus two or negative effort six. But we're not giving F of six. So it's we can't find G F four. So these are all the values filled in, so the bottom two tables, the bottom two rows are the numerical representation of G, and that is all that we have to do for this problem.


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