Chapter 2.7, Problem 22E

[M] The signal broadcast by commercial television describes each color by a vector (Y, I, Q). If the screen is black and white, only the Y-coordinate is used. (This gives a better monochrome picture than using CIE data for colors.) The correspondence between YIQ and a “standard” RGB color is given by

$\left[\begin{array}{c}Y\\ I\\ Q\end{array}\right]=\left[\begin{array}{ccc}.299& .587& .114\\ .596& -.275& -.321\\ .212& -.528& .311\end{array}\right]\left[\begin{array}{c}R\\ G\\ B\end{array}\right]$

(A screen manufacturer would change the matrix entries to work for its RGB screens.) Find the equation that converts the YIQ data transmitted by the television station to the RGB data needed for the television screen.