4. Determine a basis for Span({u, v, w}) C R, where u = (1,1,0), v =...

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4. Determine a basis for Span({u, v, w}) C R, where u = (1,1,0), v = (1,3, -1), and w = (1,-1, 1). Determine the expansion of (3, 5, -1) with respect to this basis. 5. Show that the function L: R→ R" given by L(r, y, 2) = (r+y,r+2, y+2) is a linear map, and determine ker(L) and im(L). 6. Let e = (vi, ., va) be an ordered basis of an n-dimensional vector space V, and let Le : V → K be the coordinate map given by Le(v) = (a1, a2, . an) € K", where the a, are such that v = a,v +azv, ++a,v,. Show that L. is a linear isomorphism. %3D 4. Determine a basis for Span({u, v, w}) C R, where u = (1,1,0), v = (1,3, -1), and w = (1,-1, 1). Determine the expansion of (3, 5, -1) with respect to this basis. 5. Show that the function L: R→ R" given by L(r, y, 2) = (r+y,r+2, y+2) is a linear map, and determine ker(L) and im(L). 6. Let e = (vi, ., va) be an ordered basis of an n-dimensional vector space V, and let Le : V → K be the coordinate map given by Le(v) = (a1, a2, . an) € K", where the a, are such that v = a,v +azv, ++a,v,. Show that L. is a linear isomorphism. %3D

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