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first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1 and v2 with the same...

first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1 and v2 with the same span as x1, x2. Now use the formula

p =((y, v1)/(v1, v1))v1 + ((y, v2)/(v2, v2))v2

to compute the projection of y onto that span. Of course, replace the inner product with the dot product when working with standard vectors

2)

Compute the projection of y = (1, 2, 2, 2, 1)  onto span (x1, x2) where

x1 =(1, 1, 1, 1, 1)   x2 =(4, 1, 0, 1, 4)

The inner product to use is the usual dot product. (This will compute a best-fitting function that is quadratic with no linear term, fitting to the data (−2, 1),(−1, 2),(0, 2),(1, 2),(2, 1).)

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