In the file HW09.VEC there are 7 six-dimensional vectors labeled v1,...,v6, and w. Let V be the vector space spanned by v1,...,v6. Then w is in V; write v as a linear combination of v1,...,v6. (You can't (yet) form a matrix in LINALG whose columns are v1,...,v6, and w; however, you can create a 6 by 1 matrix whose entries are all 1's (it's just v1), then augment it with v2,...,v6, and w).
Use the GRAM-SCHMIDT procedure in LINALG to find an orthonormal basis for V. You will first get an orthogonal basis - ignore it - followed by the orthonormal basis, whose vectors you should save and name as o1,...,o5. Using the procedure of Theorem 4, p. 192 of the text, find the coordinates of w relative to the basis o1,...,o5.
Extend o1,...,o5 to an orthonormal basis for R^6 by the following method. Create a random 6-dimensional vector x using LINALG and apply GRAM-SCHMIDT to o1,...,o5, and x, in that order.
