Given the vectors v1=(0,1,0,2), v2=(2,0,-1,0), v3=(2,-1,3,2)
and u=(1,-1,0,1),
Use the Gram-Schmidt process to find an orthogonal basis for the
subspace W spanned by v1, v2 and v3.
Find ProjWu, the projection of u onto the subspace W. Note:
ProjWu=α1u1+α2u2+α3u3, where the ui's are the orthogonal
vectors generated in Part (a).
Calculate the error vector u-ProjWu.
A=(v1|v2|v3), that is its columns are the vectors v1, v2, v3. Find
the solution tilde(x) of the system A^(T)Ax=A^(T)u.
Take Atilde(x) and compare it with what you got in Part (b). What
do you get?
Given the vectors v1=(0,1,0,2), v2=(2,0,-1,0), v3=(2,-1,3,2) and u=(1,-1,0,1),
Use the Gram-Schmidt process to find an orthogonal basis for the subspace W spanned by v1, v2 and v3. Find Projwu, the projection of u onto the subspace W. Note: Projwu = u + 2u2 + 3u3, where the us are the orthogonal vectors generated in Part (a).
Calculate the error vector u - Projwu.
A=(v1|v2|v3), that is its columns are the vectors v1,V2,V3. Find the solution X of the system ATAX = ATu. Take AX and compare it with what you got in Part (b). What do you get?