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12 Nov 2019
In this question, you will apply the Gram-Schmidt process. The subspace V has a basis of three vectors u_1 = (1 2 0 0), u_2 = (3 1 5 0) and u_3 (2 14 -4 1) (a) Normalise vector u_1 to give the vector v_1 (b) Find the component of u_2 orthogonal to v_1. Enter the answer exactly. This will become the vector v_2 f. ______ (C) Normalise v_2 f, to give the vector v_2. Enter the answer exactly. ______ (d) Find the component of u_3 orthogonal to both v_1 and v_2. Enter the answer exactly. This will become the vector v_2 f. ______ (e) Normalise v_2 f, to give the vector v_3. Enter the answer exactly, possibly with a square-root. For example, the squareroot of 5 is entered as squareroot (5). ______ (f) Project the vector (0 10 -16 6) onto the subspace spanned by {v_1, v_2, v_3}. _____ (g) Project the vector (-5 5 -3 2) onto the same subspace.
In this question, you will apply the Gram-Schmidt process. The subspace V has a basis of three vectors u_1 = (1 2 0 0), u_2 = (3 1 5 0) and u_3 (2 14 -4 1) (a) Normalise vector u_1 to give the vector v_1 (b) Find the component of u_2 orthogonal to v_1. Enter the answer exactly. This will become the vector v_2 f. ______ (C) Normalise v_2 f, to give the vector v_2. Enter the answer exactly. ______ (d) Find the component of u_3 orthogonal to both v_1 and v_2. Enter the answer exactly. This will become the vector v_2 f. ______ (e) Normalise v_2 f, to give the vector v_3. Enter the answer exactly, possibly with a square-root. For example, the squareroot of 5 is entered as squareroot (5). ______ (f) Project the vector (0 10 -16 6) onto the subspace spanned by {v_1, v_2, v_3}. _____ (g) Project the vector (-5 5 -3 2) onto the same subspace.
Tod ThielLv2
14 Aug 2019