Question

The RGB colour model (often an underlying system for rending colours on mobile phone and computer screens) encodes colours as vectors [r, g, b] with components representing the intensity of three primary colours [red, green, blue] that make up a given colour. For example, u = [25, 25, 100] is Midnight Blue, v = [255, 215, 0] is Gold, and w = [192, 192, 192] is Silver.

(a) Write down a system of equations to determine whether Silver is a linear combination of Midnight Blue and Gold. (Don’t solve the system in this part of the question; just write it down.)

(b) Prove that Silver is not a linear combination of Midnight Blue and Gold.

Answer 1

The solution from two equation x and y must be satisfy third equation for linear combination. Which is not happening in this solution there for it is not a linear combination.