Linear Algebra: Given the orthogonal bases v1 = [-1; 3; 1; 1], v2 = [-1, 3, 1, 1], v3 = [-1, -1, 3, -1], y = [1; 0; 0; 1], find the orthogonal projection ProjWy.

The answer given by my professor is, 1/6[3; 1; 1; -1].

I understand the equation is:

yhat = [dot(y,U1)/dot(U1,U1)]U1 + ....... [dot(y,Un)/dot(Un,Un)]Un

I did my calculations and I think the given answer is wrong and forgot to add [dot(y,U3)/dot(U3,U3)]U3, making the final answer:

0(U1)+ 1/6U2 + 1/6U3 = 1/6[2; 0; 4; -2]

Am I correct? Or am I doing something wrong here?

Question

Linear Algebra: Given the orthogonal bases v1 = [-1; 3; 1; 1], v2 = [-1, 3, 1, 1], v3 = [-1, -1, 3, -1], y = [1; 0; 0; 1], find the orthogonal projection ProjWy.

The answer given by my professor is, 1/6[3; 1; 1; -1].

I understand the equation is:

yhat = [dot(y,U1)/dot(U1,U1)]U1 + ....... [dot(y,Un)/dot(Un,Un)]Un

I did my calculations and I think the given answer is wrong and forgot to add [dot(y,U3)/dot(U3,U3)]U3, making the final answer:

0(U1)+ 1/6U2 + 1/6U3 = 1/6[2; 0; 4; -2]

Am I correct? Or am I doing something wrong here?