Find the standard matrix of an orthogonal projection
Problem 4. Let W = Span[w1; w2], where
w1 = [3 0 4]
w2 = [4 5 -3]
If T (from R^3 to R^3) is the orthogonal projection onto W, find the standard matrix of T.
I did this by finding the orthogonal projections of e1, e2, and e3 on span W and constructing the transformation from [e1 e2 e3]
My answer was :
0.680 0.400 0.240
0.400 0.500 -0.300
0.240 -0.300 0.820
Is this correct? I double checked by finding that the applying the transformation matrix to w1 and w2 returned w1 and w2 which is what it should do. Thanks!