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Moacrigiven Foy-echelon TormWrite the systemequations (or Wnich thc niven matrixquamenicc matrix- (Enter each jnswcrtcrnsX,Ya Z, and #.)+x+ 2y+ 32y-2Zw + 2(6) Usc b...

Question

Moacrigiven Foy-echelon TormWrite the systemequations (or Wnich thc niven matrixquamenicc matrix- (Enter each jnswcrtcrnsX,Ya Z, and #.)+x+ 2y+ 32y-2Zw + 2(6) Usc back-substitutionsolvc (nc Syscem(xYr z, W)4,3 1,3

moacri given Foy-echelon Torm Write the system equations (or Wnich thc niven matrix quamenicc matrix- (Enter each jnswcr tcrns X,Ya Z, and #.) +x+ 2y+ 32 y-2 Zw + 2 (6) Usc back-substitution solvc (nc Syscem (xYr z, W) 4,3 1,3



Answers

Solve each system of equations by using $A^{-1}$. Note that the matrix of coefficients in each system is a matrix from Exercises $23-44$.$ $$53$x+y+z=3$$ $$x+2 z=-4$$ $$x-y-z=-1 \quad

In an amended matrix. We have the coefficients off the variables X, y and Z to the left off the divider and the constant for each equation to the right off the divider. Each equation forms a role in the momentum matrix. For example, for the first equation, X plus six y minus one equals too negative, too. We have 16 minus one on the first roll to the left off the divider and negative two on, also on the first row to the right off the divider equation, too. Three X plus y plus four equals to seven forms. The second rule in the Elemental matrix an equation three forms if the new off the augmented matrix.

The real huge goes Jordan elimination method here. Now it's Devon. We will frustrate augmented my tricks. We get 3 to 33 four minus 571 23 minus toe. Six. Now Steptoe The Sensation first and tired little. Then they get to three minus 26 four minor. 571 3233 Now Step three. We will compute half off our want, then minus four off our one plus R two and then minus three r one plus R three to clear the first column. Now we get 13 divided by two minus 13 Geo minus 11 11 minus 11. Gentle minus five. Divided by 26 minus six. Now if their food really huge minus off one divided by 11 off our toe, then minus off. Three divided by two off. Our two plus are one and then five divided by do off our toe plus R three to clear the second column. Then we get one deal. Undivided wayto to Dwight Bebeto Deal. When minus 11 Jill Jiro. Seven. Divided by toe and minus seven, divided by two. Now if I We will compute. Motivated by seven off artery then minus one divided by two off artery plus Arman. And our three are due to clear that. God. Finally we get one. Gero Gero Gero one Gero gero gero one toe geo minus one So x equal to to buy it called the Jiro and Jericho minus one is ever final answer.

We can augment the um coefficient matrix with a constant. So we have the coefficients 32, three, Yeah, augmented with the constant three. The second equation is four X negative five Y seven Z equals one. And the third equation is two extra plus three, Y minus two. Z equals six. So once it's augmented we can do the reduced row echelon form of that matrix. What that's gonna do is row operations and then with the gauss Jordan elimination method, we've got ones and zeros and we're all said and done and that can be interpreted X is to Y is zero, Z is -1. Mhm. Mhm. Mhm.

In this problem, we have given the equations to buy his equals. Three x plus three by last, boozy as equals to 16 kind. Two weeks plus five Does the The sequence to 19. Let's consider it equation one. Immigration do on equation three. We can also ideas in equations as a is equals to 00 I think they do to buy one. B is he grew stool. So 16 I'm binding. Find Xs equals toe Thanks, my auntie. First we find a in booze. For that we right away ended my tricks He slash I now the usual operations to convert a slash I am metrics in do I slash in euros We have a mattress that is 0 to 0 33 toe to buy one slash I'd into demand tricks on the three My tree that is 100 010 001 Buying They're changing the first and taking who Armand changes to our on by using by applying the operation. I want changes to number three on one be gig run 123 0 to 0 five months Flash 01 by 30 100 zero ones now by using operations are pledging this too. Minus two R one plus R three on our do changes to one guy. Who are you? We get run, man two by three The robin zero The tree minus one. Likely flash 01 by 30 I'm going toe 00 zero minus true by 31 again by a blank progressions Our preaching in just two minus tree. Are you last hierarchy on our renting? Giusto? My news are moving us. I was. We get ones you buy. Three 010 00 minus one by three Flash minus one but one by 30 one by 200 three by two minus two Well, 31 since the first 12th call of bodies are in the desire for the moral conduct. Hard column by a blind operation. I play changes to minus three. Armand I'm Armand changes toe minus true bad three. I keep a list bigot. 100 010 The use you one slash minus seven by two minus one one by two. Do you use you nine, Michael Omar? Industry is the last metrics is in the room. I slash in goes from here. We get in. Worse is equal stool My new saving by do minus one one by two 00 My invite minus three. Now the my reply inwards and be talked in X Since Xs equals toe in verse In Toby be get X is equals toe minus seven by two minus 12 one by 200 nine by do minus three. In to be metric status, it's 16 on 19. My mind playing these two mattresses we get exes equals toe 13 and two on. We know that next match exes equals two ex my NZ from the l B Gate X equals to one. Advising was 23 on Z is equal scruple. Now we verify the result Redder excessive was to find bicycles to three and said is it was to prove that his files up given regions so that we would have to do the video X y inside in the divan equations. The fullest equation we have is Isaac was to say, by substituting, Why is it was 23 In this equation we get sex which is equals to six. So it is true. The second equation behalf iss three X plus three by plus school Z as equals to 16 minutes. After do the value of X pliancy, we get 16. It is equals to 16. So it is also true and finally living this have to do the value X, y and Z we get 19 bitches equals toe 19. So it is also true Thanks X equals to one rising goes to tree the is equals to boot said this the solution of the given equations.


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