The covariance matrix below was obtained from a Landsat image of the Columbia River in Washington, using data from three spectral bands. Let x1, x2, x3 denote the spectral components of each pixel in the image. Find a new variable of the form y1 = c1x1 + c2x2 + c3x3 that has maximum possible variance, subject to the constraint that c21 + c22 + c23 = 1. What percentage of the total variance in the data is explained by y1?
