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Problem 42

# For the following exercises, solve each system by Gaussian elimination.$$\begin{array}{l}{0.5 x-0.5 y-0.3 z=0.13} \\ {0.4 x-0.1 y-0.3 z=0.11} \\ {0.2 x-0.8 y-0.9 z=-0.32}\end{array}$$

## Discussion

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## Video Transcript

right. Question 40 to another galaxy elimination problem. Um, you see, So again, let's take a little peek in with these coefficients. Look like it looks like all three of the ex coefficients. Um, I'm going to to evenly. So I multiply the first equation sometimes for minute you. Second equation five and the third equation. I'm staying. See what? That gets me here. All right, All right. So talk equation becomes, uh, she wears minus two. Why, Um, minus 1.2 two z. You calls visits times for not going for it. Um, say four times when 13 is 52 Okay, next 12 X, um, minus 0.5. Why? Minus five. And then, um, minus 1.5 z equals point. And last one is to X minus eight. What? Minus nine. Z equals 32 3.2. All right, so now that we have this all set up, so yeah, the same number of excess and I miss attract my equations. Summers track these two. How subjective. Down. All right. What does that give me? Well, two minutes to zero. Make it two minus two minus negative. Five. Um, it's gonna be negative. two plus five. Just three. Why? Um, negative. 1.2 minus negative. 1.5. That +15 sets a B plus point. Greasy. You close? Um, 25 to minus five. It's gonna be point negative. 0.0.3 All right, I'm gonna take my next two equations. Subtract them also, and I was attracted them down. So five minus negative A who's five plus eight. So negative five plus eight. So it's gonna be three wide. Uh, you see? So we're gonna expect down here. So negative one point by minus negative nine. It's gonna be negative. 1.5 plus nine, which would be 7.5. Okay. And that equals 0.55 minus people, too. Point by five. Marchioness. Report to ISS negatives. 2.65 Okay. Um, wow, when I looked out here, um, my exits are made My wives already Same here, so I don't need to do any multiplying. I could just attract these two equations. Okay, I'm gonna subtract them. Uh, deposit disease. So 7.5 minus 23. Um, simplify My 0.37 point two. See? Equals. Negative. T 0.65 minus 0.3 So negative. 2165 minus negative. 103 gives us negative 2.62 2162 Um, divided by 7.2 equals Negative. Three point. Ah, negative 0.3 sits. Three sets. All right, So not I know that for zee, um, can solve for why color here. Okay, so let's use this equations. I get three. Why worse 0.3 signs negative 0.36 equals negative 0.3 All right, so, three, Why minus c 0.3 times is, um maybe a 0.10 eight one ones pool's mega free and 0.108 10 a non plus negative three. Who's this 1078 which divide by three. 1026 Okay, last thing to do is defined X Yes, we go back to Ah, do you what we do. So when five acts five acts minus 0.5 times 1026 minus 0.3 times mega presets equals 0.13 dances five x 15 times went 0 to 6 hands 1013 and court three times point through six is 108 He was 0.13 And then, um, move this stuff over to the other side. So I get 15 X equals 13 lows. Martyrs. Hey, 035 and X equals. All right, so my order triple this 07 I'm a 0.0 to 6. I'm a negative sense.