Linear Transformation Given by a Matrix In Exercises 23-28, define the linear transformation
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Elementary Linear Algebra (MindTap Course List)
- The Standard Matrix for a Linear Transformation In Exercises 1-6, find the standard matrix for the linear transformation T. T(x1,x2,x3,x4)=(0,0,0,0)arrow_forwardLinear Transformation Given by a Matrix In Exercises 33-38, define the linear transformations T:RnRmby T(v)=Av. Find the dimensions of Rnand Rm. A=[0110]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
- The 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_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_forwardFinding 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_forward
- Finding a Matrix for a Linear Transformation In Exercises 1-12, find the matrix Afor T relative to the basis B. T:R2R2:T(x,y)=(2xy,yx) B={(1,2),(0,3)}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 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_forward
- 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_forwardLinear Transformation Given by a Matrix In Exercises 33-38, define the linear transformations T:RnRmby T(v)=Av. Find the dimensions of Rnand Rm. A=[1213400210]arrow_forwardFinding the Kernel of a Linear Transformation In Exercise 1-10, find the kernel of the linear transformation. T:P3P2T(a0+a1x+a2x2+a3x3)=a1x+2a2x2+3a3x3arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning