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The curve $y = ax^2+bx + c$ passes through the points $(x_1, y_1), (x_2, y_2), and (x_3, y_3)$. Show that the coefficients a, b and c are a solution of the system of linear equations whose augmented matrix is:

$\left(\begin{array}{1} x_{1}^2 \quad x_{1} \quad 1 \quad y_{1}\\ x_{2}^2 \quad x_{2} \quad 1 \quad y_{2} \\ x_{3}^2 \quad x_{3} \quad 1 \quad y_{3}\end{array}\right)$

This is from Anton, Elementary Linear Algebra 9th Ed. As seen here: What does it mean to 'show that' coefficients are a solution of this system of linear equations?

I believe I have answered this question with my own answer below. Thankyou.

Harry Peter
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Bucephalus
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  • Also, I cannot post the image, only a link because I only have a reputation under 10 too. Sorry about that. – Bucephalus Jun 08 '17 at 23:57
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    We prefer it if you type the contents of the question into the page, (no images or links), and if you have further updates, you edit the original post, rather than post as an answer, or as extended comments. – Doug M Jun 09 '17 at 00:13
  • Yes, I realise the first point Doug, but I am not aware that you have a graphing function so I can draw the diagram that is related to the question. I have only done this because there is a diagram related to the question. – Bucephalus Jun 09 '17 at 00:37

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Or do I just have to put this in the form: $Xa=y$ where $a$ is vector with [a,b,c] in it? If I put it in that form, is that simply demonstrating that we will get the respective linear equations? Maybe i'm thinking too hard and that's simply the response that is required because maybe the question is interrogating that you can identify that it's linear in a,b,c and to treat the x's as constants.

Bucephalus
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  • This seems like it could be what the question is looking for. Assuming $a$ and $y$ are written as column vectors so that the matrix multiplication is justified. – WaveX Jun 09 '17 at 00:18