please show steps, thanks.

Let S = {u1, u2, u3}, with uj = [8 132- 8 8,3- 0 - S is a basis for the subspace Kof M22 consisting of all upper triangular matrices (there is no need to verify this). Use the Gram-Schmidt process on the set S to find an orthonormal basis for this subspace K. Recall that the inner product defined for two matrices U = " ] and V11 V12 is defined V21 122 (U, V) = trace(VU) = uliV11 + 212v12 + U21 721 + U22 022. You may use the following formula: If Wis a subspace with orthogonal basis { V1, V2, . . ., Vn}, then (u, v1) (u, V2) (u, Vn) projwu= 1/ V2 12 2+ . . . + Vn