Use the eigenvalue property to prove that the 2 x 2 Hessian matrix below is positive definite if and only if a + c > 0 and ac > b^2. You can use this property to help you with the remaining problems.

[a b
b c]

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option a is correct.

only one solution to the system of equations

step-by-step explanation:

if the graph of the equations do not intersects(i.,e if they are parallel) then, there are no solutions that are true for both the equations.

if the graph of the equations intersects, then there is one solution and that is true for both the equations.

since, in the given figure:

the two lines intersect each other

⇒there is only one solution which satisfy both the lines of an equations.

therefore, there is only one solution to the system of equation

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