(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

x_{1}^{2}+x_{1}x_{2}+2x_{2}^{2}=8

a) Write the equation using a quadratic form i.e. [itex]\underline{x}[/itex]^{T}A[itex]\underline{X}[/itex]=8

b)Find the Matrix Q such that the transformation [itex]\underline{X}[/itex]=Q[itex]\underline{Y}[/itex] diagonalises A and reduces the quadratic form to standard form in terms of coordinates (y_{1},y_{2})

2. Relevant equations

[itex]\underline{X}[/itex]=Q[itex]\underline{Y}[/itex]

[itex]\underline{X}[/itex]^{T}A[itex]\underline{X}[/itex]=8

3. The attempt at a solution

For question b), I got the A matrix as [1 1;0 2] or [1 0.5;0.5 2] *sorry, don't know how to use the matrix operator so I've written it matlab style*.

I used the first matrix to give a better looking eigenvalues, which resulted in 2 and 1. From the values, I got a vector of [1;0] and [1;1]

Using the vectors, I got a Q matrix of [1 0; 1/sqrt(2) 1/sqrt(2)]

and using [itex]\underline{X}[/itex]=Q[itex]\underline{Y}[/itex], I got

2.707y_{1}^{2}+2.707y_{1}y_{2}+y_{2}^{2}which I'm not even sure if its right.

Could someone please assist me in tackling this question?

Thanks!

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# Conic Equation using a Quadratic Form

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