Question

The derivative of Ax with respect to variable xp is given by __________

(a) \(\frac{d}{dx}\)(A x)=xp

(b) \(\frac{d}{dx}\)(xp)=A x

(c) ∫ A x=xp

(d) ∫xp=Ax

This question was addressed to me during an interview for a job.

This intriguing question comes from Matrix Algebra topic in section Matrix Algebra and Gaussian Elimination of Finite Element Method

Answer 1

The correct answer is (a) \(\frac{d}{dx}\)(A x)=xp

The best explanation: Let A be an (n x n) matrix of constants and x = [x1 x2 x3…… xn]^T be column vector of n variables. Then, (formula) derivative of A x with respect to variable xp is given by

\(\frac{d}{dx}\) (A x)=xp.