2. Find a basis for the subspace W = {[x y z]T : ax + by + cz = 0, a,b, c € R} of R". What is the dimension of W? 3. Let A be a square matrix, and that k1, k2 and A are scalars. Show that if Av = Xv and Aw = Xw then, A(k1v+ k2w) = X(k1v+ k2w). What can you imply about kiv+ k2w? Justify your answer. 4. Find an orthonormal basis for the subspace S = {[u v w]' : u + v = 0 and u – 2w = 0 of R".
2. Find a basis for the subspace W = {[x y z]T : ax + by + cz = 0, a,b, c € R} of R". What is the dimension of W? 3. Let A be a square matrix, and that k1, k2 and A are scalars. Show that if Av = Xv and Aw = Xw then, A(k1v+ k2w) = X(k1v+ k2w). What can you imply about kiv+ k2w? Justify your answer. 4. Find an orthonormal basis for the subspace S = {[u v w]' : u + v = 0 and u – 2w = 0 of R".
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 41CR: Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the...
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