Show that an orthogonal transformation preserves the length of
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Mathematical Methods in the Physical Sciences
Additional Math Textbook Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Probability and Statistics for Engineers and Scientists
Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
Calculus Volume 1
Mathematics for Elementary Teachers with Activities (5th Edition)
Fundamentals of Differential Equations and Boundary Value Problems
- Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.arrow_forwardFind a basis for R3 that includes the vector (1,0,2) and (0,1,1).arrow_forwardLet T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and nullity of T. (b) Find a basis for the kernel of T.arrow_forward
- Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).arrow_forwardProve that if A is similar to B and A is diagonalizable, then B is diagonalizable.arrow_forwardShow that T from Exercise 71 is represented by the matrix A=[12121212]. Proof Let T be the function that maps R2 into R2 such that T(u)=projvu, where v=(1,1) (a) Find T(x,y) (b) Find T(5,0) (c) Prove that T is a linear transformation from R2 into R2.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage