24 a Not every orthogonal set in R is linearly independent b

24. a. Not every orthogonal set in R is linearly independent b. If a set S he property that u whenever i j. then S is an orthonormal set. c. If the columns of an m x n matrix A are orthonormal, then the linear mapping x H Ax preserves lengths. d. The orthogonal projection of y onto v is the same as the orthogonal projection of y onto cv whenever e 0. e. An orthogonal matrix is invertible,

Solution

It seems that the question is of True and False

(a) False : Because orthogonal implies linear independance

(b)False: Magnitude may not be 1 so it may to be normal

(c)True: According to theorem itself

(d)True

(e)True: In orthogonal matrix the column are linear independent, so matrix is invertible