1. Color is typically described in code with 3 elements - very often, red, green, and blue, or RGB. But, a different coordinate system could be useful, such as one where overall brightness, or luminance, is one of the three components. i. Find a matrix that takes a color point described in RGB, and changes it into \"LGB\2. Playing a video game, a player tries moving into a wall at an angle. The player's velocity in the 2D playing eld is 30 represented by the vector [15] But the game will only move the player with part of this velocity, the component that moves 1 along the wall in direction [I] Find the projection of the player's velocity in this direction. 6 points 3. In a 3D remake of the same game, now the player can move into 3D walls that are at unusual angles. The player moves with 30 1 5 3D velocity 0 into a ramp parallel to the span of vectors 0 5 1 and U U 1 . Find the projection of the velocity onto the subspace described by those two vectors. Give the projection in both the original coordinate system and the coordinate system implied by the ramp's two basis vectors. (Show your work, and use fractions instead of decimals.) 10 points