Taylor Polynomial

I found the following exercise in a book. I haven’t encountered such problems before, but based on what I’ve done, determining the Taylor polynomial should be fairly easy based on the definition when we know what a is. My problem is solving the initial value problem. Maybe it could be solved with a multidimensional Chain rule…Any help would be greatly appreciated!The exerciseA smooth function :> is given with the following value and first and second derivatives at ,:.,.,,.,\begin{bmatrix}-1&-2\\-2&1\\\end{bmatrix} ( -1 2)(-2 1)A smooth function > solves the Initial Value Problem:For all ? ,,,.Determine the Taylor polynomial of the third degree of the function y at zero.Express it in the form.”Thank you very much guys!

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