Finding the Standard Matrix and the Image In Exercise
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Chapter 6 Solutions
Elementary Linear Algebra (MindTap Course List)
- Finding 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 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_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 Image In Exercises 23-26, a find the standard matrix A for the linear transformation T and b use A to find the image of the vector v. Use a software program or a graphing utility to verify your result. T(x,y,z)=(2x+3yz,3x2z,2xy+z), v=(1,2,1)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 y-axis in R2: T(x,y)=(x,y), v=(2,3).arrow_forwardThe Standard Matrix for a Linear TransformationIn Exercises 1-6, find the standard matrix for the linear transformation T. T(x,y,z)=(x+y,xy,zx)arrow_forward
- The Standard Matrix for a Linear TransformationIn Exercises 1-6, find the standard matrix for the linear transformation T. T(x,y)=(5x+y,0,4x5y)arrow_forwardLinear Transformation Given by a Matrix In Exercises 23-28, define the linear transformation T:RnRm by T(v)=Av. Use the matrix A to a determine the dimensions of Rn and Rm, b find the image of v, and c find the preimage of w. A=[2101], v=(8,4), w=(5,2).arrow_forwardLinear Transformations and Standard MatricesIn Exercises 7-18, determine whether the function is a linear transformation. If it is, find its standard matrix A. T:R3R3, T(x,y,z)=(z,y,x)arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning