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A dump of our free Chat sessions, in case it is useful. It excludes white boards used during paid sessions.

tutor3 : Hello Student, May I help you with your Math problems?
student : yes
tutor3 : say it
student : I have a question related to matrices
student : 1. Consider a kxk symmetric matrix A. a) if there exist vectors x1 and x2 such that x1'Ax>0 and x2'Ax<0, then there exist eigenvalues of A, v1 and v2, satisfying v1'Av1>0 and v2'Av2<0. Explain why.
tutor3 : is it x1'Ax or x1'Ax1?
student : x1'Ax1
student : and likewise x2Ax2<0
tutor3 : Please wait, we are helping other students
student : ok
student : having a hard time with this one?
tutor3 : no
tutor3 : you have a bit of maths to understand
student : really
student : elaborate
tutor3 : see it is x1'Ax1>0 (eq 1) .Now from the homogenous equations we know Ax1=v1*x1 .substituting Ax1 in (eq 1) we have x1'v1*x1 >0 .Now x1'x1 is A matrix since it is symetric thus we can say v1'Av1 >0 and similarly the other follows
tutor3 : Improve your grades, get 1 hour of Math coaching only $16..
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