Question

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

1)

Compute the projection of y = (1, 2, 3)  onto span (x1, x2) where

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

The inner product to use is the usual dot product

Answer 1