Finding the Standard Matrix and the Image In Exercises
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- 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_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 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 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_forwardRotate the triangle in Exercise 29 counterclockwise 90 about the point (5,3). Graph the triangles. 29. Use the standard matrix for counterclockwise rotation in R2 to rotate the triangle with vertices (3,5), (5,3) and (3,0) counterclockwise 90 about the origin. Graph the triangles.arrow_forwardFinding the Image of a Vector In Exercises 7-10, use the standard matrix for the linear transformation T to find the image of the vector v. T(x,y)=(x+y,xy,2x,2y), v=(3,3)arrow_forward
- 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_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_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
- Find a transformation matrix to rotate a vector in R2 through an angle of 30 degrees. Then use it to rotate the vector (3, 7).arrow_forwardExplain how to determine whether a function T : V → W is a linear transformation. Secondly give some example along with proper explanation where this T can be treated as matrix.arrow_forwardlinear algebraarrow_forward
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