Question

What is the index of the quadratic form, \(3x_1^2+ x_3^2+8x_{13}+ 9x_{21}+ 2x_{23}=0\)?

(a) 2

(b) 4

(c) 3

(d) 1

This question was addressed to me in final exam.

The origin of the question is Canonical Form or Sum of Squares Form topic in portion Eigen Values and Eigen Vectors of Engineering Mathematics

Answer 1

The correct answer is (a) 2

The explanation: The index of a quadratic form is the number of positive square terms.

Hence, from the given form, we have index = 2.