How can I solve a multivariable equation using

afasiask7xg

afasiask7xg

Answered question

2022-03-26

How can I solve a multivariable equation using the matrix form?
f(x,y)=x2+cy2+2xy
I want to find the values of c for the function f(x,y) has a minimum. However I have to solve it by writing the function in the following form:
f(x,y)=xyTAxy

Answer & Explanation

Lesly Fernandez

Lesly Fernandez

Beginner2022-03-27Added 16 answers

We have: f(x,y)=(x+y)2+(c1)y2. Thus if c=1, clearly the minimum is 0 when x=y. If c1, then either c<1 or c>1. For c<1, take x=y and thus f(y,y)=(c1)y2 has no minimum.
For c>1, again f(y,y)=(c1)y20 and has a minimum of 0 when y=0 and in this case x=y=0 as well. In brief, the minimum occurs for f when c1.

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