I want to learn how to do it too. But I am not finding any references for this... Can you tell me the general method to minimize functions using linear algebra as given in your text book. Or at least tell me a good reference?

And ya... I can write 4x_1^2-2x_1x_2+3x_2^2+3x_1-2x_2+1 in the matrix form... I figured out K,f and c.