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Solve the systems in Exercises $11-14$$$\begin{aligned} x_{2}+4 x_{3} &=-5 \\ x_{1}+3 x_{2}+5 x_{3} &=-2 \\ 3 x_{1}+7 x_{2}+7 x_{3} &=6 \end{aligned}$$

The matrix is inconsistent

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 1

Systems of Linear Equations

Introduction to Matrices

Cristiano D.

January 29, 2022

you're wrong

McMaster University

Harvey Mudd College

Idaho State University

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clay slits sold this set of Lena equations. No, we have three set up the immigration's here, If a question 12 and three. And to solve these as we seem we have embrace me how hair through variables X one x to an extreme and we have three minute bulls and we're three questions, which means we can solve. For the three unknowns now, a simple way to solve the three set of integrations is to take two of them in piers off, for example, everything. The 1st 2 of the 2nd 2 you saw for we tried to eliminate one off the variables. And so as toe be able to compare the other three questions now, as we can see in the question Number two and in the question Number three, we do not see the bearable X one. So let's try and eliminate X one from these two equations so as to be able to compare the first and the question that we can. So what we can do is we can take this equation and we can multiply this equation with a minus negative off. Three. Human divide This in question The negative of three. What we essentially get is we will get any into off three here. And when we add them up, we would be ending up zero or hit right Tum. So we have thanks Focus from ending in two or three x one loves. Then we multiply a negative three and dream with me mind Get off nine. Get you off nine. Thanks. Home X one and then a gain. Sorry. And then me Mum, multiply my and you get all three with five is minus 15. Extreme shouldn't be in Quito. Um, sorry. It's been driving me the metric bust. Pain has become exhaust tree and finally being get where here is, which is equal the rightness. I don't be negative off to a negative three multiply. It will become positive off six for six. So from this equation, we get from second question while deploying. Make it make it to off three. So sorry. We get this question and then we take this aggression as it is on DDE. That's right. It tome. It's fine. Write it down three times. Thinks one for us seven times. Thanks. Troll with us seven times. Thanks. Three is equal to Thanks. All right, add these three questions off left inside in the right hand side. So these two guys against loud and minus off nine plus off seven becomes minus off toe storm minus or 15 plus of seven becomes minus off aimed. Thanks. Three. And this is equal to six and six. Added up together becomes 12. So this is the question that we get from him. And then we have this equation. First question we think the first ignition and we mounted by the first a question with a negative off to know a positive off so that we can really said we can animal and her removed the 1st 0 so we get you here a minus off. Sorry, I'm sorry. Two times ex off too. Plus to wanted by before his 88 times makes off. Three mutual is equal to two multiplied by five is minus off 10. What we get over here is when we god first toe up came. So what we see is these two guys cancel out these two Alaskans love what we get is zero is equal to two, which is row Frances. It means that the system of ignitions does not have any solution Because this is never possible. Zero can never be equal to. So ideally, what we mean from here is that thes three creations This one this one and this one. They represent planes in a three dimensional access. For example, if we take Thea excess X one extraordinary and X tree And if you compare them with the normal away off three dimensions X why and z So we have a three dimensional access numbers in space and in three emission space. These three equations this 1st 1 the 2nd 1 in 3rd 1 It essentially represents a plane. And what we see from here that since there is no solution possible here, it means that these two planes do not intersect each other. Since these two planes no intersect each other, we do not have any solution. So the answer is there is no solution. No, Tony, let me Right in. Tom. No. No solution exists. This is young

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