2018-38.md

course	course_year	question_number	tags	title	year
Linear Algebra	IB	38	IB 2018 Linear Algebra	Paper 4, Section I, E	2018

Define a quadratic form on a finite dimensional real vector space. What does it mean for a quadratic form to be positive definite?

Find a basis with respect to which the quadratic form

$$x^{2}+2 x y+2 y^{2}+2 y z+3 z^{2}$$

is diagonal. Is this quadratic form positive definite?