Linear Transformations and Standard Matrices In Exercises 7-18, determine whether the function is a linear transformation. If it is, find its standard matrix A.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Elementary Linear Algebra (MindTap Course List)
- The Standard Matrix for a Linear TransformationIn Exercises 1-6, find the standard matrix for the linear transformation T. T(x,y)=(2x3y,xy,y4x)arrow_forwardLinear Transformations and Standard Matrices In Exercises 7-18, determine whether the function is a linear transformation. If it is, find its standard matrix A. T:RR2, T(x)=(x,x+2).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
- Linear Transformations and Standard MatricesIn Exercises 7-18, determine whether the function is a linear transformation. If it is, find its standard matrix A. T:R2R2, T(x,y)=(|x|,|y|)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_forwardLinear TransformationsIn Exercises 9-22, determine whether the function is a linear transformation. T:M2,2, T(A)=a+b+c+d, where A=[abcd].arrow_forward
- Finding the Inverse of a Linear TransformationIn Exercises 31-36, determine whether the linear transformation in invertible. If it is, find its inverse. T(x,y)=(x+y,3x+3y)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_forwardLinear TransformationsIn Exercises 9-22, determine whether the function is a linear transformation. T:M2,2, T(A)=b2, where A=[abcd].arrow_forward
- Finding the Kernel of a Linear Transformation In Exercises 1-10, find the kernel of the linear transformation. T:R2R2,T(x,y)=(xy,yx)arrow_forwardTrue or False? In Exercises 53 and 54, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a If T:RnRm is a linear transformation such that T(e1)=[a11,a21am1]TT(e2)=[a12,a22am2]TT(en)=[a1n,a2namn]T then the mn matrix A=[aij] whose columns corresponds to T(ei) is such that T(v)=Av for every v in Rn is called the standard matrix for T. b All linear transformations T have a unique inverse T1.arrow_forwardLinear Transformation Given by a MatrixIn Exercises 23-28, define the linear transformation T:RnRmby T(v)=Av. Use the matrix A to a determine the dimensions of Rnand Rm, b find the image of v, and c find the preimage of w. A=[100113], v=(3,5), w=(5,2,1)arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage