C) Is Tonto Rl? Why or why not? Is T 1-1? Why or why not?...

Kyle said that if $r$ is directly proportional to $s,$ then there is some non-zero constant, $c,$ such
that $r=c s$ and that $\{(s, r)\}$ is a one-to-one function. Do you agree with Kyle? Explain why or why not.

The question asks, is C three a riel vector space? Well, no, it's not a really vector space because it's a complex vector space. Um, it's going to look like a plus B. I mean, every element will look like this, and these are all complex numbers. So it's a complex vector space, not just a riel vector space.

So see, are you're seeing are so seeing artists on factorial Over minus are territorial are r factorial see in our patrol That's Victorio over minus bracket, minus R. Victoria on minus R factorial So on minus and minus R that's minus plus r good a medicine that's are so this. So this would become from factorial over our bacteria on minus r factorial. But these two are actually equal, so that's why they're the same.

In this problem of chemistry in our labs, we have given that according to Saleh Homes, one must follow the rules of scientific inquiry, gathering, observing and testing the data, then formulating, modifying and rejecting hypothesis is untamed. Only one remains did hyper did here. So look Homes use the scientific method. Why or why not? We have to tell about this. Yes settler homes used the scientific method because inside log homes investigation involves making observations. That is a gathering, collect the gathering data, then formulating a hypothesis, then testing and the hypothesis and then modifying it to the final form until one of the hypothesis is relatively. So we can say yes this is true. She is using the scientific method so we can stay here. The cell block investigation involves making observation, involves making observation. That is the gathering data, gathering data and then formulating a hypothesis. Yeah, formulating hypothesis, testing the hypothesis and modifying it. Pick until one of the hypothesis is validated until one of the hypothesis is relegated. So this is the answer. Yeah.

So here we are given an equation two X plus four Y equals 11. Were asked to say a few things about it. First, in part, they were asked to give the number of solutions. And so this isn't a system of equations, this is just a single equation. Um And if you want to look at what this equation looks like on a plot, you can rearrange it to isolate the Y. Get y equals 1/4 times negative two X plus 11 or negative one half X plus 11 4th. And you can look at the plot of this um plus 11 4th is going to be just under three. And then if the slope is negative one half we'll take forward to fall to their. And so this is what this equation looks like. And you can see that there are infinitely many points on the slide that is there are infinitely many points that satisfy this equation. If you give me any value of X, I can find a value of Y that will make this equation true. And so in a we have infinitely many part B asks us for a generalist parametric solution which we can find quite easily by taking the parameter X equals T. And then why we already rearranged our equation in the form of why over here it would just be negative one half T plus 11 4th since we're substituting in X equals teeth. And if we let T be any real number, then this is our parametric solution. Part C asks us to explain why there will never be any integer solutions to this. That is why we will never have at some point like 11 or a simple value like that. And the reason for that um you can kind of explain it in a few different ways. But um basically integer solutions are integers for X and Y. That we can plug in to make this equation true, but 11 is an odd number and any linear multiple of two and four will be even. Mhm. That is no matter how many times you add or subtract two or four, you're always going to get an even number and you're never going to be able to get 11. So this is one explanation for why you will never have integer solutions for this, and I should specify here any integer when you're multiples.