Linear Transformation Given by a Matrix In Exercises 23-28, define the linear transformation
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- Linear 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=[121101], v=(5,2,2), w=(4,2)arrow_forwardThe 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_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
- 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_forwardLet T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.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
- 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 line y=x in R2: T(x,y)=(y,x), v=(3,4).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 projection onto the vector w=(3,1) in R2:T(v)=2projwv, v=(1,4).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_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 counterclockwise rotation of 45 in R2, v=(2,2).arrow_forwardFinding the Kernel of a Linear Transformation In Exercises 1-10, find the kernel of the linear transformation. T:R3R3, T(x,y,z)=(z,y,x)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=[012114500131]arrow_forward
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