Is it manually solvabale within 1 hour? should I stop complaining and study hard or the exam itself is unfair?
>>17003095Yes, for you? No
>>17003095It looks solvable. Best do question 1 last since that one looks like it takes the longest.
>>17003095seems pretty straight forward to me, although i have no fucking clue what 3 is asking for
>>17003578Any quadratic form can be written in matrix form. Here[eqn]q(x_1,x_2,x_3,x_4) = \begin{pmatrix}x_1 & x_2 & x_3 & x_4 \end{pmatrix} \begin{pmatrix} -1 & 1 & -1 & 2 \\ 1 & 0 & -0.5 & 1 \\ -1 & -0.5 & -1 & -1 \\ 2 & 1 & -1 & 0 \end{pmatrix} \begin{pmatrix}x_1 \\ x_2 \\ x_3 \\ x_4 \end{pmatrix}[/eqn]The sign of the quadratic form is just the numbers of positive and negative eigenvalues of the matrix which with Descartes rules of signs can be determined without explicitly calculating the roots of the 4th degree polynomial.
>>17003614i'm familiar with quadratic forms and have studied them quite a bit while deriving optimization algos, just never have come across Descartes' Rule in theory or application before
>>17003095was half asleep through linear algebra past row reductions, crammed for the final and passed the course with an A. studying the theory this late is worthless, just recognize patterns and memorize how their vocab correlates to setting up problems, the rest is just row reductions and trivial formulas (no pun intended). gram-schmidt and quadratic formula questions are freebies once you have the formula down, for example.
>>17003640why even bother posting?you don't know shit about linear algebra
>>17003095Looks solvable in 1 hour. Looks like the test writer has a small penis and is intentionally making this look harder and more complicated than it should be.
>>17003095I did Descartes rule of signs in high school but don't remember it. But if the rule for it is similar for qudaratic forms, like just how it alternates + and -, then assuming I took your class it's like a 1 minute problem. For the other problems, I could've done this in high school too. Yeah it seems very doable.
>>17003767>similar for qudaratic formsIt's just the ordinary rule you learned in high school. You use it on the characteristic polynomial of the matrix.
>>17003783how do you find the polynomial for a given matrix? like the one in here−11−1210−0.51−1−0.5−1−121−10x1x2x3x4
oops i meant to say(-1. 1. -1. 2)(1. 0. -0,5. -1)(-1. -0,5. -1. -1)(2. 1. -1. 0.)
>>170037832Turns out you don't know LA either since you can't solve this
>>17003810that's impossible lol, there's no general rule for every possible set of values that could go in a matrixMatrices can be any fucking size, you think there's a way to find a polynomial that works on a 1000x1000 the same as a 4x4?
