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[-Y10 Points]DETAILSROLFFM8 2.3.026_MY NOTESTne matrix givenreduced echelon form:Write the Sysremequations represented by the Matrix_ {Usevariable~achCorres ponding...

Question

[-Y10 Points]DETAILSROLFFM8 2.3.026_MY NOTESTne matrix givenreduced echelon form:Write the Sysremequations represented by the Matrix_ {Usevariable~achCorres ponding coumin EnterX1'Xz" *_3 for Xgr andX4 )Find thc sclulicnDossiblc (Il there are inlinilcly many solulions; Express *1'Xz XaIcrnsthc paremclerthencsolution, entcr NO SOLUTION )addltlon? MaterlalaBBOC _

[-Y10 Points] DETAILS ROLFFM8 2.3.026_ MY NOTES Tne matrix given reduced echelon form: Write the Sysrem equations represented by the Matrix_ {Use variable ~ach Corres ponding coumin Enter X1' Xz" *_3 for Xgr and X4 ) Find thc sclulicn Dossiblc (Il there are inlinilcly many solulions; Express *1'Xz Xa Icrns thc paremcler thenc solution, entcr NO SOLUTION ) addltlon? Materlala BBOC _



Answers

The first screen shows the augmented matrix, A, for a nonsquare linear system of three equations in four variables, w, x, y, and z. The second screen shows the reduced row-echelon form of matrix A. For each exercise, a. Write the system represented by A. b. Use the reduced row-echelon form of A to find the system’s complete solution.

Hello, students here. We've been given two mattresses. So let's see what turned off my tresses given and then we'll discuss what they represents. So, 1st 1st rule of the first my Texas to 17 minus 23 40 zero. So this is for strove. First, my tricks. Second of this matrix is to fight 25130 13 0/3 and last choice 01 minus 230 minus two three zero. The second metrics given here is the 1st 2 is 10 105.5 zero and little second rule of this matrix 01 01 minus do zero zero the last 12 This matrix is zero zero zero one zero. Now these two mattresses are given and it is said that the 1st 2 matrix that is this matrix is it? This metrics represented augmented a question off a system of equations having four variables. And on the other hand, this is the kind of my tricks is the reduced form off This augmented my trees the first matrix. So this first mark dresses representing the system of the questions having for dinner tables and the Second Matrix is that reduced a form of the first Matrix. Now what we have to do here, we just have to form the question. The system, a few questions using the first Matrix and we have to kill cleared the value of David Abels using this second metrics. So this matrix was as I told you, this is actresses. Now let's suppose that the but he will start the blue X wiser. So W X y. So the first troubled represented cough went off the blue. The second double represented a coefficient of X. Similarly y ended, and we have to form the equation system of equations using, given my tax here. So let's form it step by step. Now for if you focus on the first True, the coefficients of W X Prize that are to 17 minus 23 40 end constant This last lawyers constant. So from this figure, the we will get the question as to w through the blue plus 17 x Let's 17 x minus 23 way minus one degree by plus 40 0 plus forties or physical +20 Right, so this is our first question. Second, the question will be caution of the Blues, too. So to the blue, I would have no and the question off excess five plus five x Let's five exit cautioned a wise one, traditionally plus away plus y plus threes. All right, three, that this is equal to zero. This is our second equation. Third and finally, question is question of the blue is zero. So this will be as it is, zero cogent off excess one. So it will start with X cogent advise minus two So minus two Y caution of that is three. So plus trees there, this is equal to zero. So these three questions are the system off the questions? Now we have to use the second test off calculate the values of the blue X wiser. So let me just first awful divide the page right here. No one thing One important one to note here is that we have only three questions because the mundane matters contest up on to the rose. So we have only three questions and the number of available. So here we have the Blue Advisor, that is for so in any case, we are not going to get a get a unique solution here. So we'll get only dependent solution. So this was the important point. The note. So you'll get only different in solution for file finding out the values off variable to independent solutions. What we will do you if you again, I will try it here. This is for caution. Some w This is for X. This is for why this is for third and last Just work off constants. Now, if you consider the year the final final rule, that is the last year caution of the blue zero, but enough x zero questioned by zero and a question of there is only one. So there is equal to a constant here. This question here is this in this race zero So this is zero. So it forced to literally of that is coming out to be zero. So this is our first well, you know, consider the little the second row Here we have coefficient of the blues are really zero. So it will be zero commission off excess. I want to caution toe off X is one This will be X coefficient of y is minus two. So this will remind us to why cautioned off their disorderly zero and constant is already zero so is equal to zero from this vigor, The value off X in terms off way Xs equals due to why so I will write it properly accessible. Go to where this is our second value as we have already discussed that they were going to get dependent solutions. Well, not getting any unique values. So we will find out the values in terms off. Why? So we get that lives there does zero We get the value off access to away now coming to the final final. No, that is the first. True. We have not considered for story. So the coefficient of from W is here one. So it will be the blue cautioned off x zero. So zero question Why is my 00.5 plus 5.5 way plus 5.5? Why the last question of the day zero and final constant is already zero. So from this *** develop the blue in terms off by the blue is equal to minus five point fight. Why, this is our what does This is our target value. This is our third and final. Very right. So we have our final dependent solutions that year and a blue X y Z This is coming out to be equal to the movie. In color too calculated the value of the blue as minus 5.5 Way. So right here minus 5.5. Why the willy off X ray of Galvin. Arrest away. So two way go. The value of why is why itself and the value off there is coming out with zero. You have already calculating the value off their that zero. So this is our solution said in terms Self. Why so? But you have assumed why as a perimeter. So this is our dependent Solutions said, depending on the value of way. So hope you understood the video and thanks for watching.

Heather in this question were given, um, the gas inform for a system of equations and the reduced row echelon form. Um, first, we're going to write what system of equations this really represents again to use variables. W X Why said and this is what they're equal to him. We can imagine there's a line in the little equal sign here, which tells us the first line reads four W minus two X plus two y minus three Zad is equal to zero. The next line will read seven w minus X minus Y minus three. Uh, that is equal to zero on the final line, reads W plus X plus y minus said, is equal to zero. And here is our system of equations. Now to solve these using the row Ashland form given, we just translate what this is saying into some equations. Um, very one tells us. W minus 1/2 Zet is equal to zero. So that's W. Is equal to 1/2. Is that Bro? To tells us. Zero times Leapt tells us X is equal to zero. Andre three tells us why minus 1/2 Zed is equal to zero. Say what this tells us is UH W is 1/2 said X is equal to zero. Why is he quitter? Half said Unsaid is equal toe zed because w. And why and said all in terms of that, we can choose a free parameter, some real number T onset, said Izzie Court T. This will give us a whole family of solutions telling us W x y zed. It's in fact, equal to half t zero ah, half t and T on here. Oh, here's the family of solutions for this set of equations. Thank you.

Today we're going. Teoh Teik Ah, the Scouse Inform on DSI what system of equations that represents and also take the ro, reduce Rochel and form of the system of equations and find the solution. Eso starting with ah system A Here we can imagine a line on a little equal sign and then to write down the system. We just note that if we use variable w, X Y and zed ah, that each number represents a coefficient. So the first line is to W plus 17 x minus 23 y plus 40 zed is equal to zero. Next is to W plus five X plus y plus three said is equal to zero and then the next line is zero x zero uh plus y minus two voters it stubby first, so zero w plus X minus two y plus three Zed is equal to zero. Um and this is thes of the system of equations that are represented. Ah, by this ah, gas and former. Now we're going to take Thea Roessler form and ah see what information this gives us. So the first row tells us W plus 5.5. Why is equal to zero or W is equal to minus 5.5. Why the next line tells us X is equal to minus two is equal to two. Why? Why this? Ah, all right, because it does X nice to is equal to zero. Then X is included to why third line tells is that is equal to zero. Putting this all together we have W is equal to minus 5.5. Why X equal to y. Why is itself and said is equities era. These three are all characterized in terms of Why So if we introduce a new free parameter, we consent wise equal t and then we have found a family of solutions. So w eggs. Why is that? Our solution is minus five foot five T to T. T and zero for tea. Some real number on hair of the solutions. Thank you.

In this video, we're going to take the scouts, inform on this reduced Rochel, inform and produce a set system of equations as well as solve that set of equations. So imagining a line and unequal site here. Andi calling the variables W X Y, and said, We read off you tro as coefficients of thes variables. So we get W plus two X plus five y plus five said, is equal to minus three W plus X plus three y plus fours that is equal to minus one interview minus X minus y plus twos. Ad is equal to three. And here's our system of equations looking each row of Theroux Eslam form in a very similar way. We'll find what information we get, so we find W plus why plus three zed is equal to one telling us W is equal to one minus y minus, Terry said. Line two tells us X Plus two y plus said, is equal to minus two or the X is equal to minus two minus two Y minus zed online three gives us no further information putting this together. We have W in terms of wine Zet one minus Y minus three Zet X in terms of wine. Zed minus two minus two. Y might have said. And why is that? This means we can introduce some free parameters if we set Why is equal to s and said is equal to tea. Then we can fully solve this system of equations W X. Why zed are equal to one minus s minus three T minus two minus two s minus T Yes, and t for S and T riel numbers than for any S and T. We confined the solutions to these equations. Thank you.


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