I) Consider V is an inner product space, and U C V a subspace. If the orthogonal projection Prv of ve V is 0, then v E U+. II) Consider R and R', with their Euclidean inner products. If T : R* → R' is is such that dim(mull T) = 2, then the orthogonal complement (range T)+ of the range of T has dimension 2. III) If the n-by-n matrix A is diagonalizable with all eigenvalues equal to 3, then A = 31, where I is the identity matrix.

I) Consider V is an inner product space, and U C V a subspace. If the orthogonal projection Prv of ve V is 0, then v E U+. II) Consider R and R', with their Euclidean inner products. If T : R* → R' is is such that dim(mull T) = 2, then the orthogonal complement (range T)+ of the range of T has dimension 2. III) If the n-by-n matrix A is diagonalizable with all eigenvalues equal to 3, then A = 31, where I is the identity matrix.

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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