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In Exercises $8-17$, graph the parametric equations after eliminating the parameter $t$. Specify the direction on the curve corresponding to increasing values of $t$. For Exercises $8-11, t$ can be any real number; for Exercises $12-17,0 \leq t \leq 2 \pi$. $$x=4 \cos 2 t, y=6 \sin 2 t$$

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.

Tell you on TV you're going Purse. Our problem Number Name Q. Did given they're extinct because to be a minus learn bright was B squared minus lor so we can't rate because explicit learned by toe substituted. Here we go. My course X plus Learn by through the war square Might Esler clearly there X plus one Oh, squared minus four Your by four. So then thanks. It was Cyril Big right? Because minus three by four, then a when y equals zero Pretty good, Because why the street going that What? So the point, sir, X light x zero minus three before why you feel so learn by zero minus three For the graph We'll look like this is what this is too minus one minus two minus three bar. So coffee look like this? Their send off our question that

Colored todavia going to start problem number. He did, given that its peak was they squared minus look, but it was depressed. It's already got right. Three square because Ex Placement substituted here. Play Because who off? It's best one, but it's like and it's because zero you get Blake was no. When. Why? It was by by God's group off explicit lunch this one's cladding. All right, uh, there for lead off explicitly, then. 16 acres. Extreme Islam squatting mother ex papers with. So I record it, Sir Cyril, I want to find it. They're being God, not fight. So the graph can be drawn us one today, Prue play by doing 50. So fusty. Cyril Kamar zero called Want or this one And you feel off 15 off floating love can be missile That is there about four question. Thanks

Hello, Dave are today We're going to start problem number. They're deep here X because Bruce, I d. On light because three costea So this coverage in us saying, Because exabyte do And this country that's close to the coast wide by three quiet expired through the whole square plus bye bye reader who square in close sine squared d plus gosquared at the square by full Does wife called by mine It comes from you decide. It's so you can brother think autograph. We look like this. This one will be plus three plus two minus do my industry but this is looking out for ridicule.