In electronic systems, colours can be displayed according to the RGB model as triples(x1, x2, x3) where x1 represents the intensity of the primary colour red, x2 represents the intensity of the primary colour green, and x3 represents the intensity of the primary colour blue. These are the primary colours of light, and in most electronic systems,the values ofx1, x2, x3 are restricted to integers between 0 and 255. The triple (0,0,0)represents the lowest intensity of all colours, which is black as it appears on a screen,while (255,255,255) would represent the highest intensity of all of the light beams combined, and appears as white on a screen. (255,0,0) produces the colour red, but other combinations may also look (to us) to be red; for example, (200,100,100) looks like the colour red too, but the intensity and light balance is different.

The official brand colours ******* for are:

Future Blue:F= (0,60,113)

Simcoe Blue:S= (0,119,202)

Tech Tangerine:T= (231,93,42)

For (a) and (b), please use MATLAB for any calculations that are needed. Answers can be written in decimal form, but please include four significant digits.

(a) (5 marks) Theoretically speaking, would it be possible to represent all RGB colours as FST colours instead?

Note:This is possible if the vectors F,S, and T would work as a new coordinate system. That is, show that any RGB vector (x1, x2, x3) can be written uniquely as a linear combination of F,S, and T, or show that its not possible.

*(b) (2 marks) The official ******* Blue is rgb (0,76,155). Write ******* Blue as a linear combination of the FST colors instead.

(c) (3 marks) Give a reason why the set of RGB colours is not a subspace ofR3.Which axioms do not hold?