Finding the Image of a
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Elementary Linear Algebra (MindTap Course List)
- Finding the Standard Matrix and the Image In Exercises 11-22, a find the standard matrix A for the linear transformation T, b use A to find the image of the vector v, and c sketch the graph of v and its image. T is the reflection in the y-axis in R2: T(x,y)=(x,y), v=(2,3).arrow_forwardProof Let A be an nn square matrix. Prove that the row vectors of A are linearly dependent if and only if the column vectors of A are linearly dependent.arrow_forwardFinding the Standard Matrix and the Image In Exercises 11-22, a find the standard matrix A for the linear transformation T, b use A to find the image of the vector v, and c sketch the graph of v and its image. T is the reflection in the line y=x in R2: T(x,y)=(y,x), v=(3,4).arrow_forward
- Finding the Standard Matrix and the ImageIn Exercises 11-22, a find the standard matrix A for the linear transformation T, b use A to find the image of vector v, and c sketch the graph of v and its image. T is the reflection in the origin in R2: T(x,y)=(x,y), v=(3,4).arrow_forwardGiving a Geometric Description In Exercises 45-50, give a geometric description of the linear transformation define by the elementary matrix. A=[2001]arrow_forwardFinding the Standard Matrix and the Image In Exercises 11-22, a find the standard matrix A for the linear transformation T, b use A to find the image of the vector v, and c sketch the graph of v and its image. T is the counterclockwise rotation of 45 in R2, v=(2,2).arrow_forward
- Proof Prove that if matrix A is diagonalizable, then AT is diagonalizable.arrow_forwardFinding the Standard Matrix and the Image In Exercise 11-22, a find the standard matrix A for the linear transformations T, b use A to find the image of the vector v, and c sketch the graph of v and its image. T is the projection onto the vector w=(3,1) in R2:T(v)=2projwv, v=(1,4).arrow_forwardFinding the Standard Matrix and the Image In Exercise 11-22, a find the standard matrix A for the linear transformations T, b use A to find the image of the vector v, and c sketch the graph of v and its image. T is the reflection in the vector w=(3,1) in R2:T(v)=2projwvv, v=(1,4).arrow_forward
- Orthogonal Diagonalization In Exercises 41-46, find a matrix P that orthogonally diagonalizes A. Verify that PTAP gives the correct diagonal form. A=[120210005]arrow_forwardTrue or false? det(A) is defined only for a square matrix A.arrow_forwardProofProve that if A is not square, then either the row vectors of A or the column vectors of A form a linearly dependent set.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning