SOLVED:Find a 3 ×3 orthogonal matrix P whose first two rows are multiples of u1=(1,1,1) and u2=(0,-1,1), respectively. (Note that, as required, u1 and u2 are orthogonal.) First find a nonzero vector u3 orthogonal to u1 and u2 ; say (cross product) u3=u1 ×u2=(2,-1,-1). Let A be the matrix whose rows are u1, u2, u3 ; and let P be the matrix obtained from A by normalizing the rows of A. Thus, A=[ 1 1 1 0 -1 1 2 -1 -1 ] and P=[ 1 / √(3) 1 / √(3)

Orthogonal Matrices - Examples with Solutions

Finding the vector orthogonal to the plane — Krista King Math | Online math help