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Problem 24

For the following exercises, solve each system by Gaussian elimination.

$$

\begin{aligned} 5 x-3 y+4 z &=-1 \\-4 x+2 y-3 z &=0 \\-x+5 y+7 z &=-11 \end{aligned}

$$

Answer

The system of equations has no solution because $0 \neq-2$

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## Discussion

## Video Transcript

All right, um, solve this using gallops combination. Right. So, um, one way in which did try Thio do these problems is it's very like, crank it out sort of way. What you do is just pick a variable and make all all the equations have the same coefficient for that. So prints on this one, I could take the exes, and I can change five for negative one. They all go into 20. All right, So I'm gonna make first this second and the third equation all start with 20 X. All right, so this equation gets multiplied by four. This equation gets multiplied by negative five. This equation gets multiplied by 20. Okay, um, now it's copy down the result of that. So the top equation becomes 20 acts minus 12. What? Plus 16 z equals negative. Four cases, four times each of the terms. Negative. Five times a second. Equation 20 x. Yeah, I'm negative. Five times. Tubes. Why? And then Positive. 15. Not a legal 0500 The last one negative. One times. Bigger twins, 20 x. You're minus 100 watt minus 1 40 c equals a positive. Teach one. All right. And So now I have that I can combine these. So what I'm gonna do is I'm on this track. We're here, tracked them, and I think I'll subtract them. You a second equation, meister, Percy. It's a 20 mile 20 miles. 20 0 Um, negative. 10 minus negative. Well, it's positive too. Why? And then 15 minus 16 ISS negative one. See? And then zero. Minus negative for posit. Yeah. Now I'm gonna do the same thing with 2nd 2 equations. 20 minus 20 homeless. Attract them. Me. See, I think they'll subtract these down the second equation. Minds for separation. So again, I have no access. Negative. 10 minus negative. 100. It's 90 and then 15 minus negative. 14 is 155. See? Equals two twin. Right? And so for this one now I want you Is by this equation, hours here, most by this equation by five make the wise both be 97 90. Why, um, minus 45. See? Equals money up 90 times two. So there it's a track. Please bridge in something. Subtract them down. Euro ones for closet War one. How do we got here? Just double check this thing. This is right. Um, so that is 90 55 zero. 00 minus 2 20 It's negative. All right, Better. Okay, so, um, spoke through. We have, uh, since he will subtract those, it's a tracked them down. So 90 Mind signing 01 55 minus negative. 45 is 200 z equals negative. 20 minus one eighties negative. 400 Bible size by 200 z. Negative, too. Yeah. Yeah. Nice. Remember? So now I need to go back and find out what other variables are. So let's use this equation to find why, and so I get to Why minus see needles for so too. Why Bus too. Vehicles for And two, Why equals two and watch what? So no X and y Last thing to do is defined. See, I could take any of my way. I mean, I'm sorry to find X. Um, some of his last operation. It is just as a negative accident. So negative x plus five times. Why? Just one plus seven mimzy, which is negative too together equals negative. 11. All right, so we get negative, X. Um, plus five minus 14 equals negative. 11. You'd be so native X. Um, this night, 11 and nine to both sides and negative. That's equal at 92 So that means X equals two. Um, and my order Triple B two one. You too, right?

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