Can someone please help me with this matrix ? I have been working on it for 4 hours and its not working.
2x+y+4z=15 2x+3y+z=-6 2x-y+2z=12
I worked it out, but the last step is not working out. Please help

- anonymous

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- tkhunny

What are you trying to do?

- anonymous

Trying to find the point of intersection using matrices

- anonymous

yes, I worked on it for 4 hours. Its a high school class. It has taken up most of my time from studying for exams

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## More answers

- tkhunny

Here's a plan...never do that. Frustration kills the value of such an exercise.
\[\left[\begin{matrix}2 & 1 & 4 & 15 \\ 2 & 3 & 1 & -6 \\ 2 & -1 & 2 & 12 \end{matrix}\right]\]
You got this.

- anonymous

yes. I know. But it just annoys me that I can't get it.

- anonymous

thats what I got

- tkhunny

\[\left[\begin{matrix}2 & 1 & 4 & 15 \\ 0 & 2 & 3 & -21 \\ 0 & 2 & 2 & 3 \end{matrix}\right]\]
How about this? Using the upper left as the first pivot?

- anonymous

shouldn't the 2 and 3 in the second row be negative? and the 2 2 3 in the 3rd also be negative. because i turned the 2 in the upper left into 1 first then got the two number number to be 0

- tkhunny

0 -2 -2 -3 or 0 2 2 3, it is of no consequence.
Note this. What is the difference in these solution?
- x - y = -12
vs
x + y = 12

- tkhunny

Are we agreed, yet?

- anonymous

sure go on

- tkhunny

Okay, then using the middle '2' as pivot, we get:
\[\left[\begin{matrix}2 & 0 & 11/2 & 51/2\\ 0 & 2 & -3 & -21\\ 0 & 0 & 5 & 24\end{matrix}\right]\]

- anonymous

yes

- tkhunny

Then the '5', after simply dividing the third row by 5.
\[\left[\begin{matrix}2 & 0 & 0 & -9/10 \\ 0 & 2 & 0 & -33/5 \\0 & 0 & 1 & 24/5 \end{matrix}\right]\]

- anonymous

yes. wait. what I'm having a problem with is getting the second row. I have the 0 1 0 but I don't get the -33/10

- tkhunny

Do you still have '2' over in the middle? I left it a '2'. Divide by 2 to get -33/10 instead of -33/5.

- anonymous

I did it a different way tho

- tkhunny

That's fine. Unique answers don't care how you find them.

- anonymous

But i'm making a mistake and I don't know were it is, because mine takes 9 steps to do, and my 9th step i can't get -33/10

- tkhunny

You will have to figure out how to code your result or take pictures. I can't see through the screen, right? :-)

- anonymous

yea I know. Could I type out what i did and you see were i went wrong

- anonymous

\[\left[\begin{matrix}1 & 1/2 & 2 & 15/2 \\ 0 & 2 & -3 & -21 \\ 0 & -2 & -2 & -3 \end{matrix}\right]\]
So first I multiplied row one by 1/2. Then subtracted row 2 from 2 multiplied by row 1. Then subtracted row 3 from 2 multiplied by row 1

- tkhunny

That looks good.

- anonymous

\[\left[\begin{matrix}1 & 0 & 11/4 & 15/4 \\ 0 & 1 & -3/2 & -21/2 \\ 0 & 0 & -5 & -24 \end{matrix}\right]\]
So here I first multiplied row two by 1/2. Then subtracted row 1 from 1/2 multiplied by row 2. Then I added row 3 from 2 multiplied by row 2

- tkhunny

Whoops! There it is. s/b 51/4, not 15/4.

- anonymous

\[ \left[\begin{matrix}1 & 0 & 0 & -9/20 \\ \\ 0 & 0 & 1 & 24/5 \end{matrix}\right]\]

- anonymous

I know I typed it wrong

- anonymous

I have 51/2 on my page

- tkhunny

51/4?

- anonymous

its my second row thats a problem . Sorry again. 51/4 not 51/2

- tkhunny

Okay, looking good so far, after we cleared up 51/4.

- anonymous

So to get the last one I posted, I multiplied the third row by -1/5. Then I subtracted row 1 from 11/4 multiplied by row 3 . But for my second row when I try to add row 2 to 3/4 multiplied by row 3. I don't get -33/10

- tkhunny

3/4? Another typo? This should be 3/2.

- anonymous

OMG I COPIED IT WRONG UGHHHHH.

- tkhunny

We found it?

- anonymous

YEA. I REALLY HATE THIS!!!!!

- tkhunny

A little fanfare may be in order. Really, just slow down a little and don't try to skip steps. When I do this I am very careful to WRITE all subtractions and additions off to the side and reconstruct the entire matrix at each step. I also try to avoid fractions by waiting to divide some things.
You'll get the hang of it. Keep the faith and hang in there!

- anonymous

I have show all my steps, and I do my addition and subtraction on the side. But I have them in rows and the matrix that I work on last I should copy again and start working on again, but I looked at 11/4 and thought that -3/2 was also -3/4. I spent all of my free class working on this, my lunch, then after school. Then at home. I didn't even study for exams today. Thanks for your help

- tkhunny

Yikes. Well, maybe more lunch will help. :-) Sorry, no magic wand, Just have to keep at it
Excellent work hanging in there. Sometimes perseverance wins the day. Of course, sometimes it drives you a little crazy, first.

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