Colors on a computer are represented using RGB vectors, representing the intensity of red, green, and blue light (the three colors used in computer screens). Pure red is the vector (1,0,0), pure green is (0,1,0), and pure blue is (0,0,1). Another way of representing colors is the XYZ vector, which has less physical significance, but corresponds better to the way humans perceive color. Assuming the RGB values are correctly normalized, the XYZ vector is a linear function of the RGB vector. Suppose pure red has an XYZ value of (41.2,21.3,0.2), pure green has an XYZ value of (35.7,71.5,11.9), and pure blue has an XYZ value of (18.0,7.2,95.0). Write the 3 x 3 matrix which converts from RGB to XYZ. If lavender has the RGB vector (0.462,0.209,0.716), what is its XYZ vector