# Matrix of a Parabola? (It's my first day)

SpeeDFX
Hi guys, I started linear algebra just yesturday. I've read the first section of the first chapter and now I'm trying to do some problems from this section and I'm stuck on #7. I scanned the page from my math book (here's a link: http://img392.imageshack.us/img392/8476/lach11n72fb.jpg [Broken]). After reading this section of my book, I'm pretty sure I understand what an "augmented matrix" is. I understand what "consistent" means, and also understand the basic row operations.

In an attempt to figure out what the question is asking, I wrote down their augmented matrix in equation form, and I wrote the following.

y1 = ax1^2 + bx1 + c
y2 = ax2^2 + bx2 + c
y3 = ax3^2 + bx3 + c

Even if this isn't in the right direction to solving the problem, did I do this correctly?

I'm confused as to what exactly the question is asking, and what to "show". I've always been bad at the questions that ask to "show" something is true or false. Please help!

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## Answers and Replies

Homework Helper
Looks like you almost have it. Yes, those equations are the ones corresponding to the given augmented matrix. Now, do you see that those are precisely the equations stating that (x1,y1), (x2, y2), (x3,y3) are on the parabola y= ax2+ bx+ c?

SpeeDFX
HallsofIvy, I do see and understand that, although I'm having trouble understanding why or how that answers the question in the second phrase. Could you explain to me what the second phrase is asking me to do? Sorry for all the questions. This whole thing is totally new to me.

jaggy
Bump.

I've run into the same problem from the same book. I understand that the stated equations are for each x,y point, however I'm not sure how to proceed!