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R4= RyFna Lha Bus € Jlod Ki0) Econ 2.5 _ 1Euiusund = 1 1 3 1813...

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R4= RyFna Lha Bus € Jlod Ki0) Econ 2.5 _ 1Euiusund = 1 1 3 1813

R4= RyFna Lha Bus € Jlod Ki0) Econ 2.5 _ 1 Euiusund = 1 1 3 1 8 1 3



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Exer $1-8:$ Find, if possible, $A+B, A-B, 2 A,$ and $-3 B$ $$A=\left[\begin{array}{rr} 6 & -1 \\ 2 & 0 \\ -3 & 4 \end{array}\right], \quad B=\left[\begin{array}{rr} 3 & 1 \\ -1 & 5 \\ 6 & 0 \end{array}\right]$$

Notice Fine whether it is concerned, not so. Drop battle lane the y axis any object it got at once. So any land pedal to the Y axis if cutting graph points. So it is not difference and because for every below X we're getting to a low upward and downward. So port every. Have a look off X. There are toe value off Funston. Therefore, it is not fun. It isn't our defenses. And if you talk about Domine soared amendments all the way. Low Xer call the doorman sort of a woman. It's from minus four before. If you object all the way low. OPEC's carriageway often is from minus four to port on the range. Rains are often develop, which is from minus three to today, so this is stomach and range.

In this video, we're gonna go through the answer to question number 17 from chapter 9.4. So we asked to find where these vectors x one x two x three Ah, linearly dependent on where they are linearly independence, which FYI is teeth independent much varsity that linearly dependent. So okay, so for them to be linearly dependent would need values off. See one c two c three it such that c one times x one c two times x two plus C three times Next three equal to zero association into values for these x one x two x three then we write This is a system of three equations. So the 1st 1 is just gonna be Ah, well, it's the the first element of each of the equations Time each of the vectors X one experience to text three times by the corresponding um constant C one C to C three. So we're gonna have Well, there's no, uh, ex threes are no component, Maxime, because the top of the next three is zero. So we're going off, uh, ex one next Tuesday, at both of which contain eats the to tease it. So take a common factor out. Get either to t C one plus C two. Ah equals there. Next up, we're gonna have eats the two tea. Close. It was C one that's actually to eat the TT plus C three he to the three tea equal Syria. And finally five. Easter to tee times five C one minus C two equals Sarah. Okay, so comparing the first of these equations on the last of these equations we find that C one don't see too must be equal to zero as you see that because, well, first look in the first equation e to the two tea for any tea can never be zero. So we basically just cancel by its beauty and saying with the bottom equation s So therefore, we have this bit is equal to zero this busy zero for those two to both equal to zero. Then C one and C t o. You can show that by rearranging one of those sub student in the other. Um and you're find this. You wanna see t birthday frequent zero. So therefore I see two is the rocks that this is zero. So then we have to see three times Three tier sequence There we can we can divide by eats and three team because that's never zero for any tea on DDE. All we're left with is C three sequences So far, all t ah the C one c to the T three. Must could only be for this for this equation. Thio be satisfied. Uh, this equation to be satisfied then Theo Dissolution of the Trivial Solution. Therefore the vectors x one x two x three are linearly independent for that tea in any value between minus infinity to infinity.

In this question we have to find the metrics product A. B and B. Both here. So, first of all, I am finding the metrics product. That is A. B here. Okay, so I am providing the values of metrics and be here. So you can see that metrics is given to us. That is in the first of all, 30 minus one. In the second of 04 In the 3rd, double 5 -3 and one. Okay, similarly, here we have 140 and minus five and then one and minus one. Okay, and here, zero minus two and three. Now we have to multiply here. So we can see that. First of all, we have to multiply this first of all here with the first column means we can say that three with 130 with 40 and minus one. Mhm Zero here. Okay, So again, I can say they're 20. Not with the 2nd column. So it provides me three with minus five minus 15 0 with 010 minus one with minus 11 With the third column it provides three with 000 with minus 20 minus one with three minus three. Okay, similarly we are google this for the second column. Also second go with again all the columns. So zero with one here, 04 with 4 30 16, two with zero. That is zero with the second column. Zero with minus 504 with 14 and two with minus one minus two. With the third column, zero with 00 and four with minus two minus eight. Okay, two with 36 Now we take here the third go here again. Hardball with first follow then five with 1, -3 with four minus 12. 1 with 00 Now with the second column, five with minus five minus 25 minus three with one minus 31 with minus one minus one in the third column five years, 00 minus three minus 26 And one with three. That is three. Okay. Now you even say that You get the first element that is three years, okay? And this element is -14. And further we get -3 Here 16 9 here too. And Next Fit -2 and 5 -12. That is, We can say that. Yeah. Five minutes to always there due to the reason because we have to multiply five with one. We get here five and minus three with four. We got your 12. Okay. And five minus 12, results in two minus seven. Okay And minus 25 minus three minus four. That is minus 29 6 with three. That is nine. Okay, so this is the product to be here. Now I have to also find the product can be also. So I can say that or B. We have to put first of all be and after that we have to put the metrics area. Okay, so I can say that my matrix B was one minus 50 and 41 minus two and zero minus 13 metallic say was Today 0 -1. Zero for two. 5 -3. 1. Okay, now we can say that we are going to multiply here. Okay. First of all, did this? First problem means one way 33 minus five with zero, 00 with 50 Okay, now with the second column one with 00 minus five. With four minus 20 0 with minus 30 Now with the third column minus one minus 10 And zero. Okay, now the second row will first fallen 43, 12 one with zero. That is zero minus two with minus crab. That is minus 10. With the second column four were 001 week four. Okay -2 with -30. That is six. With the 3rd column four with -1 -4. 1 and two. That is to and minus two and one that is minus two. And now with the third Hello? With the first column that is zero and 30 minus one and 00 three and five. That is 15. Now with the second column zero and 00 minus one and four minus 43 and minus three minus nine. Now with the third column zero and minus 10 minus one and two minus 23 and one. That is three years. Okay. Now you can see that we get here. Finally that is three in the the first element. Okay. And you can see The Second Element is -20 year. Okay? and the 3rd element should be minus of 11 and here's well minus 10. That is to six plus four, that is 10. And here we get -4. Okay. Further look at here 15 and minus of 13 and one hobby. So this is the value of being here.

Okay for this question. What I have done is I have X values and ethics values of Rebecca is essentially the exact same thing is why sort of diners have put this model into an online graphing calculator. And I've graphed it using accent half of axe essentially, And you can see over here that it clearly falls all adjust it growth model. It's going up like this men, meaning that it is growth.


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