Question

What is the signature of the quadratic form, \(Q = 7x_1^2+ 2x_2^2- 3x_3^2+x_{31}+ x_{23}=0\)?

(a) 2

(b) -2

(c) 1

(d) -1

This question was posed to me during a job interview.

My query is from Canonical Form or Sum of Squares Form topic in section Eigen Values and Eigen Vectors of Engineering Mathematics

Answer 1

The correct answer is (c) 1

Explanation: We know that signature is the difference between the number of positive and negative square terms of a quadratic form. Therefore, we have signature = 2 – 1 = 1.