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Solve using a graphing utility’s
REF or RREF
command:
$$\left\{\begin{aligned} 2 x_{1}-2 x_{2}+3 x_{3}-x_{4} =12 \\ x_{1}+2 x_{2}-x_{3}+2 x_{4}-x_{5} =-7 \\ x_{1}+ x_{3}+x_{4}-5 x_{5}=1 \\-x_{1}+x_{2}-x_{3}-2 x_{4}-3 x_{5} =0 \\ x_{1}-x_{2} x_{4}+x_{5}= 4\end{aligned}\right.$$

I'm using the desk most matrix calculator. So we're going to say we have a new matrix is going to be since we have x 1234 and five. And then the constants That it's six columns and um five rows. So we're doing a five row by six column where the coefficients are too negative two, three negative one zero. And it's augmented with the constant 12. And then the second equation would be one x one positive two X two minus one X three plus two X four -1 x five equals negative seven. Third equation one X sub to know anyone except one. No except to one except 31 except four negative five. X some five with the constant one 4th equation negative one x 1 positive one X two negative one X three negative two X four negative three X five equals zero. And the fourth or to me the fifth equation one x 1 -1 x two. No x three negative one X four in positive one X five equals four. Okay once that is stored then you can reduce wrote um Echelon four Matrix A and interpret X sub one equals one. Except two equals negative one. X sub three equals two. X sub four equals negative two and X sub five equals zero.

Hello and welcome to this video solution of numerous. Here we are given a link comprehension. So here in statement one were given that and iron or a on roasting with sodium carbonate and lying in the presence of air gives to compound PNC. And you're from option the second part the solution be in concentrated. It's alan reaction with production furrows and it gives a blue color on precipitated of compound their cost solution of C. On treatment with considerate statistical gives a yellow colored compound E. And the compound even treat it with a seal gives an orange red compound F. Which is used as an ox raise anything. So you have to make certain predictions to come into the solution. So let me show you how it's made. So first of all we take for if he oh she had to poetry thus eight and a two freedom global neck And with air that is given seven or 2 good line gives you to a free two or three that's eight the name so Seattle four. That's it. It's a frustration. Next we have if we two or three reacting with concentrate sales that is given gives you who official three Last three H 2. Right now this official tree reacts with who before if he 10 6 that is protection fellow sign a great this gives you the blue solution pushing blue solution of if the four if he CN six whole trade plus 12 cases. Mm Next From three we have two any he wanted to see our well for That's 8/10 of food gives you we need to the odd 47 is the yellow color solution. Greatness in A. Two so four. That's it too. No you have in A to see our two or seven. Okay, last case here is the orange color substance of people pr two or seven that's 2010. So this is the so let us state what is A what is B. The first we have me is If you see a 23, this is a Next we have every two or 3 SCB or Yes. So this suits also be ready And in in 204 this is C. Right BNC. That is mentioned. Yes. Now this pushing blue books. Mhm. Yeah. Yeah. Whoa it is. Mhm. Okay. To see again this election with the this one your local er this is E and we have orange. What are some common? It does if Yeah. Right. I hope this is clear to you and have a very good rest of the day. Thank you.

Statement who is correct? Because n. c. -1. Let's n. c. r. is actually same as endless one. c. r. It's a very important for me actually it's very easy to prove. So what we do is we take the left hand side. The plant is in factorial by n minus R plus one factorial into ar minus one factorial. And this is in fact a well by end minus our factory into R. Factorial. So what will take common? So let's take common first the right length. In fact well by end minus R. Plus one in two and minus R. Factorial into our minus on factory in plus N. Factorial by end minus our factory into our into our minus one fatto. So then let's take common. We can take common in factorial by n minus R. Factorial into our -1 factorial in Bracket. What we get is one by n minus R. Plus one plus one bite. Uh huh. So let's take calcium in the bracket. So it becomes in factorial by N minus R. Factoring into ar minus two factorial. So when you take and see him you need to be in place one do not need to be in minus R. Plus one into art. But what is in fact a leading to N plus one? It is N plus one factorial divided by what is N minus R. Factory. And doing minus or plus one is n minus R. Plus one factory. In our into our minus one factories are factories. So which is nothing But and plus one C. R. So statement to is correct. Now let's use this formula and find the value of 15 c. four plus 15 C. Five plus 16 C six. 15 C four plus 15 to 5 will be 16 C. Five. Because in this and his 15 R. S. Endless one cr 16 five. Now that is getting added to 16 6 now here in in 60 RS six, so it should be 17 C six, but right hand side is actually given us 17 67 17 C six is not same as 17 C seven. In fact it is same as 1711. Alright, so statement one is wrong and statement tweets Okay?

I have even so in this question they asked the second in addition energy of the carbon nitrogen option. And flooring atoms are such as is carbon far far greater than nitrogen far far greater than flooring for greater than carbon bees. Flooring greater than option greater than nitrogen greater than carbon C. Is carbon greater than night auction greater than nitrogen greater than deep. Please oxygen greater than floating greater than nitrogen greater than got a button so yeah. Option dis correct. Yeah. Option beads curry nine days, 9 days the second ionization energy of carbon nitrogen option flooring are yeah, The 2nd Innovation and Adultery of carbon nitrogen option and flooring are in the older Yes, yeah auction greater than flooring which is greater than nitro ocean. This is greater than carbon. Yeah. Yeah. Yeah. Yeah. Yeah. Mhm. Half fill two P three sub shell of a plus is highly stable, highly stable then stable compared to compared two to be force sub selloff. Yes. Yeah. Of a plus sold. I used to of folks who is young will be larger than f minus. Yeah. No Jeff then eight minus. Thanks lot.